diff --git a/.travis.yml b/.travis.yml
index f3790dc0804..bb4ce0fb9fb 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,160 +1,42 @@
 language: rust
 sudo: false
 
-# We support too many combinations of Rust releases, crate features, operating
-# systems, and architectures to even remotely test all combinations.
-# Yet it turns out we can test most of these independent of each other, because
-# they serve different goals or test different pieces of code.
-#
-# RUST RELEASES
-# Goal: make sure we don't use language features unavailable on a certain
-#       version, and build without warnings.
-# We have different builders use 4 Rust releases, a pinned stable release,
-# the latest stable, beta and nightly.
-#
-# ARCHITECTURES
-# Goal: test against issues caused by differences in endianness, pointer sizes,
-#       etc.
-# We run tests on 4 different architectures.
-# - x64_84, default on Travis (Linux) and AppVeyor (Windows)
-# - i686, second AppVeyor (Windows) configuration
-# - MIPS, big-endian Linux emulated with QEMU (thanks to Trust)
-# - ARMv7, Android emulated with QEMU (thanks to Trust)
-#
-# OPERATING SYSTEMS
-# Goal: test on many operating systems, to verify the OsRng code, which is
-#       mostly architecture-independent.
-# We run tests on Linux, OS X, Windows, Android (emulated), and Node.js (using
-# cargo-web).
-# One builder cross-compiles for many of the remaining OSes, which ensures we
-# keep building, but doesn't run tests.
-# OSes supported by Rand but which we can't cross-compile because there
-# is no pre-built standard library available: Dragonfly BSD, Haiku, OpenBSD.
-#
-# CRATE FEATURES, TESTS, AND SUB-CRATES
-# Goal: Run unit tests, doctests, examples, and test benchmarks for all crates,
-#       in configurations that cover all interesting combinations of features.
-# Tests run on rand:
-# - test no_std support, but only the unit tests:
-#   `cargo test --tests --no-default-features`
-# - test no_std support, including the alloc feature:
-#   cargo test --tests --no-default-features --features=alloc
-# - run unit tests and doctests with all features which are available on stable:
-#   `cargo test --features=serde1,log`
-# - test examples:
-#   `cargo test --examples`
-# Additional tests on nightly:
-# - run unit tests and doctests with all features which are available on nightly:
-#   `cargo test --all-features`
-# - run benchmarks as tests:
-#   `cargo test --benches --features=nightly`
-# Tests on subcrates:
-# - select crates via --manifest-path (more reliable than --package)
-# - test appropriate feature matrix
-#
-# TODO: SIMD support on stable releases
-# NOTE: SIMD support is unreliable on nightly; we track the latest release
-# NOTE: Test for alloc feature in no_std is not included here because it depends
-#       on the alloc crate stabilized in Rust 1.36.
+# Since most OS-specific code has moved to the getrandom crate, we require
+# few target-specific tests here.
+
 matrix:
   include:
     - rust: 1.32.0
-      env: DESCRIPTION="Linux, 1.32.0"
+      name: "Linux, 1.32.0"
+      env: ALLOC=0
       os: linux
-      script:
-        # Differs from standard script: rand_pcg features
-        - cargo test --tests --no-default-features
-        # TODO: add simd_support feature:
-        - cargo test --features=serde1,log
-        - cargo test --examples
-        - cargo test --manifest-path rand_core/Cargo.toml
-        - cargo test --manifest-path rand_core/Cargo.toml --no-default-features
-        - cargo test --manifest-path rand_distr/Cargo.toml
-        - cargo test --manifest-path rand_isaac/Cargo.toml --features=serde1
-        # TODO: cannot test rand_pcg due to explicit dependency on i128
-        - cargo test --manifest-path rand_xorshift/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_xoshiro/Cargo.toml
-        - cargo test --manifest-path rand_chacha/Cargo.toml
-        - cargo test --manifest-path rand_hc/Cargo.toml
-        - cargo test --manifest-path rand_jitter/Cargo.toml
-        - cargo test --manifest-path rand_os/Cargo.toml
-
-    - rust: 1.32.0
-      env: DESCRIPTION="OSX, 1.32.0"
-      os: osx
-      script:
-        # Differs from standard script: rand_pcg features
-        - cargo test --tests --no-default-features
-        # TODO: add simd_support feature:
-        - cargo test --features=serde1,log
-        - cargo test --examples
-        - cargo test --manifest-path rand_core/Cargo.toml
-        - cargo test --manifest-path rand_core/Cargo.toml --no-default-features
-        - cargo test --manifest-path rand_distr/Cargo.toml
-        - cargo test --manifest-path rand_isaac/Cargo.toml --features=serde1
-        # TODO: cannot test rand_pcg due to explicit dependency on i128
-        - cargo test --manifest-path rand_xorshift/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_xoshiro/Cargo.toml
-        - cargo test --manifest-path rand_chacha/Cargo.toml
-        - cargo test --manifest-path rand_hc/Cargo.toml
-        - cargo test --manifest-path rand_jitter/Cargo.toml
-        - cargo test --manifest-path rand_os/Cargo.toml
 
     - rust: stable
-      env: DESCRIPTION="Linux, stable"
+      name: "Linux, stable"
 
     - rust: stable
-      env: DESCRIPTION="OSX+iOS, stable"
+      name: "OSX+iOS, stable"
       os: osx
       install:
         - rustup target add aarch64-apple-ios
       script:
-        # Differs from standard script: includes aarch64-apple-ios cross-build
-        - cargo test --tests --no-default-features
-        # TODO: add simd_support feature:
-        - cargo test --features=serde1,log
-        - cargo test --examples
-        - cargo test --manifest-path rand_core/Cargo.toml
-        - cargo test --manifest-path rand_core/Cargo.toml --no-default-features
-        - cargo test --manifest-path rand_distr/Cargo.toml
-        - cargo test --manifest-path rand_isaac/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_pcg/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_xorshift/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_xoshiro/Cargo.toml
-        - cargo test --manifest-path rand_chacha/Cargo.toml
-        - cargo test --manifest-path rand_hc/Cargo.toml
-        - cargo test --manifest-path rand_jitter/Cargo.toml
-        - cargo test --manifest-path rand_os/Cargo.toml
+        - bash utils/ci/script.sh
         - cargo build --target=aarch64-apple-ios
 
     - rust: beta
-      env: DESCRIPTION="Linux, beta"
+      name: "Linux, beta"
 
     - rust: nightly
       os: linux
-      env: DESCRIPTION="Linux, nightly, docs"
+      name: "Linux, nightly, docs"
+      env: NIGHTLY=1
       install:
         - cargo --list | egrep "^\s*deadlinks$" -q || cargo install cargo-deadlinks
         - cargo deadlinks -V
       before_script:
         - pip install 'travis-cargo<0.2' --user && export PATH=$HOME/.local/bin:$PATH
       script:
-        # Differs from standard script: all features, doc build
-        - cargo test --tests --no-default-features --features=alloc
-        - cargo test --all-features
-        - cargo test --benches --features=nightly
-        - cargo test --examples
-        - cargo test --manifest-path rand_core/Cargo.toml
-        - cargo test --manifest-path rand_core/Cargo.toml --no-default-features --features=alloc
-        - cargo test --manifest-path rand_distr/Cargo.toml
-        - cargo test --manifest-path rand_isaac/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_pcg/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_xorshift/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_xoshiro/Cargo.toml
-        - cargo test --manifest-path rand_chacha/Cargo.toml
-        - cargo test --manifest-path rand_hc/Cargo.toml
-        - cargo test --manifest-path rand_jitter/Cargo.toml
-        - cargo test --manifest-path rand_os/Cargo.toml
+        - bash utils/ci/script.sh
         # remove cached documentation, otherwise files from previous PRs can get included
         - rm -rf target/doc
         - cargo doc --no-deps --all --all-features
@@ -162,103 +44,20 @@ matrix:
       after_success:
         - travis-cargo --only nightly doc-upload
 
-    - rust: nightly
-      os: osx
-      env: DESCRIPTION="OSX, nightly, docs"
-      install:
-        - cargo --list | egrep "^\s*deadlinks$" -q || cargo install cargo-deadlinks
-        - cargo deadlinks -V
-      script:
-        # Differs from standard script: all features, doc build
-        - cargo test --tests --no-default-features --features=alloc
-        - cargo test --all-features
-        - cargo test --benches --features=nightly
-        - cargo test --examples
-        - cargo test --manifest-path rand_core/Cargo.toml
-        - cargo test --manifest-path rand_core/Cargo.toml --no-default-features --features=alloc
-        - cargo test --manifest-path rand_distr/Cargo.toml
-        - cargo test --manifest-path rand_isaac/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_pcg/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_xorshift/Cargo.toml --features=serde1
-        - cargo test --manifest-path rand_xoshiro/Cargo.toml
-        - cargo test --manifest-path rand_chacha/Cargo.toml
-        - cargo test --manifest-path rand_hc/Cargo.toml
-        - cargo test --manifest-path rand_jitter/Cargo.toml
-        - cargo test --manifest-path rand_os/Cargo.toml
-        # remove cached documentation, otherwise files from previous PRs can get included
-        - rm -rf target/doc
-        - cargo doc --no-deps --all --all-features
-        - cargo deadlinks --dir target/doc
-
-    - rust: nightly
-      env: DESCRIPTION="WASM via emscripten, stdweb and wasm-bindgen"
-      install:
-        - rustup target add wasm32-unknown-unknown
-        - rustup target add wasm32-unknown-emscripten
-        - nvm install 9
-        - ./utils/ci/install_cargo_web.sh
-        - cargo web prepare-emscripten
-        - cargo web -V
-        - cargo list | grep install-update || cargo install -f cargo-update
-        - cargo install-update -i cargo-update wasm-bindgen-cli wasm-pack
-      addons:
-        chrome: stable
-      script:
-        # Testing wasm32-unknown-emscripten fails because of rust-lang/rust#49877
-        # However, we can still build and link all tests to make sure that works.
-        # This is actually useful as it finds stuff such as rust-random/rand#669
-        - EMCC_CFLAGS="-s ERROR_ON_UNDEFINED_SYMBOLS=0" cargo web test --target wasm32-unknown-emscripten --no-run
-        #- cargo web test --target wasm32-unknown-emscripten
-        #- cargo web test --nodejs --target wasm32-unknown-emscripten
-        #- cargo build --target wasm32-unknown-unknown # without any features
-        - cargo build --target wasm32-unknown-unknown --features=wasm-bindgen
-        - cargo web test --target wasm32-unknown-unknown --features=stdweb
-        - cargo build --manifest-path tests/wasm_bindgen/Cargo.toml --target wasm32-unknown-unknown
-        - wasm-bindgen --nodejs target/wasm32-unknown-unknown/debug/rand_wasm_bindgen_test.wasm --out-dir tests/wasm_bindgen/js
-        - node tests/wasm_bindgen/js/index.js
-        - wasm-pack test --node tests/wasm_bindgen
-
-    - rust: nightly
-      env: DESCRIPTION="cross-platform builder (doesn't run tests)"
-      install:
-        - rustup target add x86_64-sun-solaris
-        - rustup target add x86_64-unknown-cloudabi
-        - rustup target add x86_64-unknown-freebsd
-        #- rustup target add x86_64-unknown-fuchsia
-        - rustup target add x86_64-unknown-netbsd
-        - rustup target add x86_64-unknown-redox
-      script:
-        # Test the top-level crate with all features:
-        - cargo build --target=x86_64-sun-solaris --all-features
-        - cargo build --target=x86_64-unknown-cloudabi --all-features
-        - cargo build --target=x86_64-unknown-freebsd --all-features
-        #- cargo build --target=x86_64-unknown-fuchsia --all-features
-        - cargo build --target=x86_64-unknown-netbsd --all-features
-        - cargo build --target=x86_64-unknown-redox --all-features
-
-    # Trust cross-built/emulated targets. We must repeat all non-default values.
-    - rust: stable
-      sudo: required
-      dist: trusty
-      services: docker
-      env: DESCRIPTION="Linux (MIPS, big-endian)" TARGET=mips-unknown-linux-gnu
-      install:
-        - sh utils/ci/install.sh
-        - source ~/.cargo/env || true
-      script:
-        - bash utils/ci/script.sh
+    # This target catches endianness issues
     - rust: stable
       sudo: required
       dist: trusty
       services: docker
-      env: DESCRIPTION="Android (ARMv7)" TARGET=armv7-linux-androideabi
+      name: "Linux (MIPS, big-endian)"
+      env: TARGET=mips-unknown-linux-gnu
       install:
         - sh utils/ci/install.sh
         - source ~/.cargo/env || true
-      script:
-        - bash utils/ci/script.sh
+
+    # This target checks we really can build no_std binaries
     - rust: nightly
-      env: DESCRIPTION="no_std platform test"
+      name: "no_std platform test"
       install:
         - rustup target add thumbv6m-none-eabi
       script:
@@ -267,44 +66,35 @@ matrix:
 
     - rust: nightly
       os: linux
-      env: DESCRIPTION="Miri, nightly"
+      name: "Miri, nightly"
       script:
         - sh utils/ci/miri.sh
+    
+    - rust: nightly
+      os: linux
+      name: "Minimal dep versions"
+      script:
+        - cargo generate-lockfile -Z minimal-versions
+        - bash utils/ci/script.sh
 
 before_install:
   - set -e
   - rustup self update
 
 script:
-  - cargo test --tests --no-default-features
-  - cargo test --tests --no-default-features --features getrandom
-  - cargo test --tests --no-default-features --features=alloc
-  # TODO: add simd_support feature:
-  - cargo test --features=serde1,log
-  - cargo test --examples
-  - cargo test --manifest-path rand_core/Cargo.toml
-  - cargo test --manifest-path rand_core/Cargo.toml --no-default-features
-  - cargo test --manifest-path rand_core/Cargo.toml --no-default-features --features=alloc
-  - cargo test --manifest-path rand_distr/Cargo.toml
-  - cargo test --manifest-path rand_isaac/Cargo.toml --features=serde1
-  - cargo test --manifest-path rand_pcg/Cargo.toml --features=serde1
-  - cargo test --manifest-path rand_xorshift/Cargo.toml --features=serde1
-  - cargo test --manifest-path rand_xoshiro/Cargo.toml
-  - cargo test --manifest-path rand_chacha/Cargo.toml
-  - cargo test --manifest-path rand_hc/Cargo.toml
-  - cargo test --manifest-path rand_jitter/Cargo.toml
-  - cargo test --manifest-path rand_os/Cargo.toml
+  - bash utils/ci/script.sh
 
 after_script: set +e
 
-cache:
-  cargo: true
-  directories:
-    - .local/share/cargo-web
+# Cache: this seems to do more harm than good
+#cache:
+  #cargo: true
+  #directories:
+    #- .local/share/cargo-web
 
-before_cache:
-  # Travis can't cache files that are not readable by "others"
-  - chmod -R a+r $HOME/.cargo
+#before_cache:
+  ## Travis can't cache files that are not readable by "others"
+  #- chmod -R a+r $HOME/.cargo
 
 env:
   global:
diff --git a/Cargo.toml b/Cargo.toml
index b87559abdfe..2cc2d9181d8 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -60,7 +60,7 @@ rand_pcg = { path = "rand_pcg", version = "0.2", optional = true }
 # This is a dependency because: we forward wasm feature flags
 # This is renamed because: we need getrandom to depend on rand_core/getrandom
 getrandom_package = { version = "0.1.1", package = "getrandom", optional = true }
-log = { version = "0.4", optional = true }
+log = { version = "0.4.4", optional = true }
 
 [dependencies.packed_simd]
 # NOTE: so far no version works reliably due to dependence on unstable features
diff --git a/appveyor.yml b/appveyor.yml
index ef0b4bff66b..a4cfbeed61d 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -32,12 +32,14 @@ install:
 build: false
 
 test_script:
-  - cargo test --tests --no-default-features --features alloc
-  # TODO: use --all-features once simd_support is sufficiently stable:
+  - cargo test --tests --no-default-features
+  - cargo test --tests --no-default-features --features=alloc,getrandom
+  # all stable features:
   - cargo test --features=serde1,log
   - cargo test --benches --features=nightly
   - cargo test --examples
   - cargo test --manifest-path rand_core/Cargo.toml
+  - cargo test --manifest-path rand_core/Cargo.toml --no-default-features
   - cargo test --manifest-path rand_core/Cargo.toml --no-default-features --features=alloc
   - cargo test --manifest-path rand_distr/Cargo.toml
   - cargo test --manifest-path rand_isaac/Cargo.toml --features=serde1
@@ -46,4 +48,5 @@ test_script:
   - cargo test --manifest-path rand_xoshiro/Cargo.toml
   - cargo test --manifest-path rand_chacha/Cargo.toml
   - cargo test --manifest-path rand_hc/Cargo.toml
+  - cargo test --manifest-path rand_jitter/Cargo.toml
   - cargo test --manifest-path rand_os/Cargo.toml
diff --git a/rand_distr/Cargo.toml b/rand_distr/Cargo.toml
index 315a5b06095..3eab050ef9c 100644
--- a/rand_distr/Cargo.toml
+++ b/rand_distr/Cargo.toml
@@ -24,4 +24,6 @@ rand = { path = "..", version = "0.7" }
 [dev-dependencies]
 rand_pcg = { version = "0.2", path = "../rand_pcg" }
 # Histogram implementation for testing uniformity
-average = "0.9.2"
+average = "0.10.0"
+# Not a direct dependency but required to boost the minimum version:
+conv = "0.3.2"
diff --git a/rand_isaac/Cargo.toml b/rand_isaac/Cargo.toml
index c11c305ab17..a63ab18147e 100644
--- a/rand_isaac/Cargo.toml
+++ b/rand_isaac/Cargo.toml
@@ -23,9 +23,11 @@ serde1 = ["serde", "rand_core/serde1"]
 
 [dependencies]
 rand_core = { path = "../rand_core", version = "0.5" }
-serde = { version = "1", features = ["derive"], optional = true }
+serde = { version = "1.0.63", features = ["derive"], optional = true }
+# Not a direct dependency but required to boost the minimum version:
+serde_derive = { version = "1.0.63", optional = true }
 
 [dev-dependencies]
 # This is for testing serde, unfortunately we can't specify feature-gated dev
 # deps yet, see: https://github.com/rust-lang/cargo/issues/1596
-bincode = "1"
+bincode = "1.1.4"
diff --git a/utils/ci/script.sh b/utils/ci/script.sh
index 852a850bd3c..bd011d57d58 100644
--- a/utils/ci/script.sh
+++ b/utils/ci/script.sh
@@ -2,23 +2,56 @@
 
 set -ex
 
+# ----- Options -----
+
+# TARGET enables cross-building
+if [ -z $TARGET ]; then
+    CARGO=cargo
+else
+    CARGO=cross
+    TARGET="--target $TARGET"
+fi
+
+# ALLOC defaults on; is disabled for rustc < 1.36
+if [ -z $ALLOC ]; then
+    ALLOC=1
+fi
+
+# NIGHTLY defaults off
+
+
+# ----- Script -----
+
 main() {
-    cross test --target $TARGET --tests --no-default-features
-  # TODO: add simd_support feature:
-    cross test --target $TARGET --features=log
-    cross test --target $TARGET --examples
-    cross test --target $TARGET --manifest-path rand_core/Cargo.toml
-    cross test --target $TARGET --manifest-path rand_core/Cargo.toml --features=serde1
-    cross test --target $TARGET --manifest-path rand_core/Cargo.toml --no-default-features
-    cross test --target $TARGET --manifest-path rand_distr/Cargo.toml
-    cross test --target $TARGET --manifest-path rand_isaac/Cargo.toml --features=serde1
-    cross test --target $TARGET --manifest-path rand_pcg/Cargo.toml --features=serde1
-    cross test --target $TARGET --manifest-path rand_xorshift/Cargo.toml --features=serde1
-    cross test --target $TARGET --manifest-path rand_xoshiro/Cargo.toml --features=serde1
-    cross test --target $TARGET --manifest-path rand_chacha/Cargo.toml
-    cross test --target $TARGET --manifest-path rand_hc/Cargo.toml
-    cross test --target $TARGET --manifest-path rand_os/Cargo.toml
-    cross test --target $TARGET --manifest-path rand_jitter/Cargo.toml
+  if [ "0$NIGHTLY" -ge 1 ]; then
+    $CARGO test $TARGET --all-features
+    $CARGO test $TARGET --benches --features=nightly
+  else
+    # all stable features:
+    $CARGO test $TARGET --features=serde1,log,small_rng
+  fi
+
+  if [ "$ALLOC" -ge 1 ]; then
+    $CARGO test $TARGET --tests --no-default-features --features=alloc,getrandom,small_rng
+    $CARGO test $TARGET --manifest-path rand_core/Cargo.toml --no-default-features --features=alloc
+  fi
+  
+  $CARGO test $TARGET --tests --no-default-features
+  $CARGO test $TARGET --examples
+  
+  $CARGO test $TARGET --manifest-path rand_core/Cargo.toml
+  $CARGO test $TARGET --manifest-path rand_core/Cargo.toml --no-default-features
+  $CARGO test $TARGET --manifest-path rand_core/Cargo.toml --no-default-features --features=getrandom
+  
+  $CARGO test $TARGET --manifest-path rand_distr/Cargo.toml
+  $CARGO test $TARGET --manifest-path rand_isaac/Cargo.toml --features=serde1
+  $CARGO test $TARGET --manifest-path rand_pcg/Cargo.toml --features=serde1
+  $CARGO test $TARGET --manifest-path rand_xorshift/Cargo.toml --features=serde1
+  $CARGO test $TARGET --manifest-path rand_xoshiro/Cargo.toml
+  $CARGO test $TARGET --manifest-path rand_chacha/Cargo.toml
+  $CARGO test $TARGET --manifest-path rand_hc/Cargo.toml
+  $CARGO test $TARGET --manifest-path rand_jitter/Cargo.toml
+  $CARGO test $TARGET --manifest-path rand_os/Cargo.toml
 }
 
 # we don't run the "test phase" when doing deploys