diff --git a/libm-test/src/generate/edge_cases.rs b/libm-test/src/generate/edge_cases.rs
index 2fb074638..4e4a782a1 100644
--- a/libm-test/src/generate/edge_cases.rs
+++ b/libm-test/src/generate/edge_cases.rs
@@ -51,6 +51,7 @@ where
 
     // Check some special values that aren't included in the above ranges
     values.push(Op::FTy::NAN);
+    values.push(Op::FTy::NEG_NAN);
     values.extend(Op::FTy::consts().iter());
 
     // Check around the maximum subnormal value
diff --git a/libm-test/src/precision.rs b/libm-test/src/precision.rs
index f6cdd015a..32825b15d 100644
--- a/libm-test/src/precision.rs
+++ b/libm-test/src/precision.rs
@@ -444,13 +444,18 @@ fn binop_common<F1: Float, F2: Float>(
     expected: F2,
     ctx: &CheckCtx,
 ) -> CheckAction {
-    // MPFR only has one NaN bitpattern; allow the default `.is_nan()` checks to validate. Skip if
-    // the first input (magnitude source) is NaN and the output is also a NaN, or if the second
-    // input (sign source) is NaN.
-    if ctx.basis == CheckBasis::Mpfr
+    // MPFR only has one NaN bitpattern; skip tests in cases where the first argument would take
+    // the sign of a NaN second argument. The default NaN checks cover other cases.
+    if ctx.base_name == BaseName::Copysign && ctx.basis == CheckBasis::Mpfr && input.1.is_nan() {
+        return SKIP;
+    }
+
+    // FIXME(#939): this should not be skipped, there is a bug in our implementationi.
+    if ctx.base_name == BaseName::FmaximumNum
+        && ctx.basis == CheckBasis::Mpfr
         && ((input.0.is_nan() && actual.is_nan() && expected.is_nan()) || input.1.is_nan())
     {
-        return SKIP;
+        return XFAIL_NOCHECK;
     }
 
     /* FIXME(#439): our fmin and fmax do not compare signed zeros */
diff --git a/libm-test/src/test_traits.rs b/libm-test/src/test_traits.rs
index 2af6af60b..278274d91 100644
--- a/libm-test/src/test_traits.rs
+++ b/libm-test/src/test_traits.rs
@@ -312,12 +312,9 @@ where
     let mut inner = || -> TestResult {
         let mut allowed_ulp = ctx.ulp;
 
-        // Forbid overrides if the items came from an explicit list, as long as we are checking
-        // against either MPFR or the result itself.
-        let require_biteq = ctx.gen_kind == GeneratorKind::List && ctx.basis != CheckBasis::Musl;
-
         match SpecialCase::check_float(input, actual, expected, ctx) {
-            _ if require_biteq => (),
+            // Forbid overrides if the items came from an explicit list
+            _ if ctx.gen_kind == GeneratorKind::List => (),
             CheckAction::AssertSuccess => (),
             CheckAction::AssertFailure(msg) => assert_failure_msg = Some(msg),
             CheckAction::Custom(res) => return res,
@@ -327,9 +324,20 @@ where
 
         // Check when both are NaNs
         if actual.is_nan() && expected.is_nan() {
-            if require_biteq && ctx.basis == CheckBasis::None {
+            // Don't assert NaN bitwise equality if:
+            //
+            // * Testing against MPFR (there is a single NaN representation)
+            // * Testing against Musl except for explicit tests (Musl does some NaN quieting)
+            //
+            // In these cases, just the check that actual and expected are both NaNs is
+            // sufficient.
+            let skip_nan_biteq = ctx.basis == CheckBasis::Mpfr
+                || (ctx.basis == CheckBasis::Musl && ctx.gen_kind != GeneratorKind::List);
+
+            if !skip_nan_biteq {
                 ensure!(actual.biteq(expected), "mismatched NaN bitpatterns");
             }
+
             // By default, NaNs have nothing special to check.
             return Ok(());
         } else if actual.is_nan() || expected.is_nan() {
diff --git a/libm/src/math/copysign.rs b/libm/src/math/copysign.rs
index d2a86e7fd..d093d6107 100644
--- a/libm/src/math/copysign.rs
+++ b/libm/src/math/copysign.rs
@@ -59,9 +59,17 @@ mod tests {
 
         // Not required but we expect it
         assert_biteq!(f(F::NAN, F::NAN), F::NAN);
-        assert_biteq!(f(F::NEG_NAN, F::NAN), F::NAN);
+        assert_biteq!(f(F::NAN, F::ONE), F::NAN);
+        assert_biteq!(f(F::NAN, F::NEG_ONE), F::NEG_NAN);
         assert_biteq!(f(F::NAN, F::NEG_NAN), F::NEG_NAN);
+        assert_biteq!(f(F::NEG_NAN, F::NAN), F::NAN);
+        assert_biteq!(f(F::NEG_NAN, F::ONE), F::NAN);
+        assert_biteq!(f(F::NEG_NAN, F::NEG_ONE), F::NEG_NAN);
         assert_biteq!(f(F::NEG_NAN, F::NEG_NAN), F::NEG_NAN);
+        assert_biteq!(f(F::ONE, F::NAN), F::ONE);
+        assert_biteq!(f(F::ONE, F::NEG_NAN), F::NEG_ONE);
+        assert_biteq!(f(F::NEG_ONE, F::NAN), F::ONE);
+        assert_biteq!(f(F::NEG_ONE, F::NEG_NAN), F::NEG_ONE);
     }
 
     #[test]