diff --git a/AstSemantics.md b/AstSemantics.md
index 63b25248..c7df3aa1 100644
--- a/AstSemantics.md
+++ b/AstSemantics.md
@@ -524,14 +524,15 @@ When the result of any arithmetic operation other than `neg`, `abs`, or
 the implicit leading digit of the significand) of the NaN are computed as
 follows:
 
- - If the operation has any NaN input values, implementations may select any of
-   them to be the result value, but with the most significant bit of the
-   fraction field overwritten to be 1.
-
- - If the implementation does not choose to use an input NaN as a result value,
-   or if there are no input NaNs, the result value has a nondeterministic sign
-   bit, a fraction field with 1 in the most significant bit and 0 in the
-   remaining bits.
+ - If the fraction fields of all NaN inputs to the instruction all consist
+   of 1 in the most significant bit and 0 in the remaining bits, or if there are
+   no NaN inputs, the result is a NaN with a nondeterministic sign bit, 1 in the
+   most significant bit of the fraction field, and all zeros in the remaining
+   bits of the fraction field.
+
+ - Otherwise the result is a NaN with a nondeterministic sign bit, 1 in the most
+   significant bit of the fraction field, and nondeterminsitic values in the
+   remaining bits of the fraction field.
 
 32-bit floating point operations are as follows:
 
diff --git a/Rationale.md b/Rationale.md
index e47e24b9..e0971f5e 100644
--- a/Rationale.md
+++ b/Rationale.md
@@ -340,23 +340,20 @@ architectures there may be a need to revisit some of the decisions:
 ## NaN bit pattern propagation
 
 In general, WebAssembly's floating point operations provide the guarantee that
-a NaN returned from an operation won't have new bits set in its fractional
-field, except the most significant bit.
+if all NaNs passed to an operation are "canonical", the result is "canonical",
+where canonical means the most significant bit of the fraction field is 1, and
+the trailing bits are all 0.
 
 This is intended to support interpreters running on WebAssembly that use
-NaN-boxing, because they can rely on the property that if an arithmetic
-operation has no non-canonical NaNs as input, its output is also canonical.
-
-The specific bit-pattern rules are modeled after what numerous popular
-hardware architectures do. Note that IEEE 754-1985 had looser rules for NaN
-bit pattern encodings than IEEE 754-2008, and some hardware architectures,
-notably MIPS, historically behaved differently than other architectures.
-However, since the publication of IEEE 754-2008, MIPS has added a configuration
-mode (NAN2008) which enables support for the new rules.
-
-In particular, the sign bit of generated NaNs is nondeterministic since x86
-generates NaNs with it set to 1 while other architectures generate NaNs with it
-set to 0.
+NaN-boxing, because they don't have to canonicalize the output of an arithmetic
+instruction if they know the inputs are canonical.
+
+When the inputs are non-canonical, the resulting NaN is nondeterministic, to
+accomodate a variety of known hardware behaviors: returning one of the input
+NaNs, returning a canonical NaN, or bitwise-or'ing the input NaNs together.
+
+The sign bit of generated NaNs is always nondeterministic since x86 generates
+NaNs with it set to 1 while other architectures generate NaNs with it set to 0.
 
 
 ## Integer operations