diff --git a/ml_dtypes/include/float8.h b/ml_dtypes/include/float8.h
index e073b84f..ad286861 100644
--- a/ml_dtypes/include/float8.h
+++ b/ml_dtypes/include/float8.h
@@ -61,13 +61,13 @@ class float8_base {
 
   template <typename T>
   explicit EIGEN_DEVICE_FUNC float8_base(
-      T f, std::enable_if_t<std::is_arithmetic_v<T>, int> = 0)
-      : float8_base(ConvertFrom(static_cast<float>(f)).rep(),
+      T i, std::enable_if_t<std::is_integral_v<T>, int> = 0)
+      : float8_base(ConvertFrom(static_cast<float>(i)).rep(),
                     ConstructFromRepTag{}) {}
-  explicit EIGEN_DEVICE_FUNC float8_base(double f64)
-      : float8_base(ConvertFrom(f64).rep(), ConstructFromRepTag{}) {}
-  explicit EIGEN_DEVICE_FUNC float8_base(float f32)
-      : float8_base(ConvertFrom(f32).rep(), ConstructFromRepTag{}) {}
+  template <typename T>
+  explicit EIGEN_DEVICE_FUNC float8_base(
+      T f, std::enable_if_t<std::is_floating_point_v<T>, int> = 0)
+      : float8_base(ConvertFrom(f).rep(), ConstructFromRepTag{}) {}
   explicit EIGEN_DEVICE_FUNC float8_base(Eigen::bfloat16 bf16)
       : float8_base(ConvertFrom(bf16).rep(), ConstructFromRepTag{}) {}
   explicit EIGEN_DEVICE_FUNC float8_base(Eigen::half f16)
@@ -112,10 +112,10 @@ class float8_base {
 
   // Conversions allowing saturation and truncation.
   template <bool kSaturate = false, bool kTruncate = false, typename From>
-  static inline EIGEN_DEVICE_FUNC Derived ConvertFrom(const From& from);
+  static inline EIGEN_DEVICE_FUNC Derived ConvertFrom(From from);
 
   template <typename To, bool kSaturate = false, bool kTruncate = false>
-  static inline EIGEN_DEVICE_FUNC To ConvertTo(const Derived& from);
+  static inline EIGEN_DEVICE_FUNC To ConvertTo(Derived from);
 
   // Operators via float32.
   EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Derived
@@ -634,7 +634,8 @@ struct numeric_limits_float8_e4m3fnuz : public numeric_limits_float8_base {
   }
   static constexpr float8_e4m3fnuz infinity() {
     return float8_e4m3fnuz::FromRep(0x80);
-  }  // NaN.
+  }
+  // NaN.
   static constexpr float8_e4m3fnuz quiet_NaN() {
     return float8_e4m3fnuz::FromRep(0x80);
   }
@@ -1239,13 +1240,38 @@ struct ConvertImpl<float8_e5m2, Eigen::half, kSaturate, kTruncate> {
 
 template <typename Derived>
 template <bool kSaturate, bool kTruncate, typename From>
-EIGEN_DEVICE_FUNC Derived float8_base<Derived>::ConvertFrom(const From& from) {
-  return ConvertImpl<From, Derived, kSaturate, kTruncate>::run(from);
+EIGEN_DEVICE_FUNC Derived float8_base<Derived>::ConvertFrom(const From from) {
+  // We are rounding double/long double -> float -> float8. This can induce
+  // double-rounding which may alter the results. We can correct for this using
+  // a trick explained in: Boldo, Sylvie, and Guillaume Melquiond. "When double
+  // rounding is odd." 17th IMACS World Congress. 2005.
+  if constexpr (std::is_floating_point_v<From> &&
+                sizeof(From) > sizeof(float)) {
+    // binary64, float80, binary128, etc. end up here.
+    static_assert(std::numeric_limits<From>::digits >=
+                  std::numeric_limits<float>::digits + 2);
+    static_assert(std::numeric_limits<float>::min_exponent >=
+                  std::numeric_limits<From>::min_exponent + 2);
+    static_assert(std::numeric_limits<float>::radix == 2);
+    float from_rnd_float = static_cast<float>(from);
+
+    // Round-to-odd involves us setting the LSB if we dropped any bits while
+    // rounding.
+    if (std::isfinite(from_rnd_float) &&
+        static_cast<From>(from_rnd_float) != from) {
+      from_rnd_float = Eigen::numext::bit_cast<float>(
+          Eigen::numext::bit_cast<uint32_t>(from_rnd_float) | 1);
+    }
+    return ConvertImpl<float, Derived, kSaturate, kTruncate>::run(
+        from_rnd_float);
+  } else {
+    return ConvertImpl<From, Derived, kSaturate, kTruncate>::run(from);
+  }
 }
 
 template <typename Derived>
 template <typename To, bool kSaturate, bool kTruncate>
-EIGEN_DEVICE_FUNC To float8_base<Derived>::ConvertTo(const Derived& from) {
+EIGEN_DEVICE_FUNC To float8_base<Derived>::ConvertTo(const Derived from) {
   return ConvertImpl<Derived, To, kSaturate, kTruncate>::run(from);
 }
 
diff --git a/ml_dtypes/tests/float8_test.cc b/ml_dtypes/tests/float8_test.cc
index b8dbb685..765428b8 100644
--- a/ml_dtypes/tests/float8_test.cc
+++ b/ml_dtypes/tests/float8_test.cc
@@ -407,6 +407,40 @@ TYPED_TEST(Float8Test, ConvertTo) {
   }
 }
 
+template <typename SrcType, typename IntermediateType, typename Float8>
+static SrcType DoubleRoundHelper() {
+  // If we have a number of the form 1.0..010..010.., two rounds of RTNE can
+  // cause the last-set bit to get rounded down due to RTNE which in turn will
+  // cause the other bit to get rounded down due to RTNE. RTNE's tie breaking
+  // semantics *should* not apply here as there is no tie but double-rounding
+  // may confuse us.
+  SrcType x{1.0};
+  x += std::ldexp(SrcType{1.0}, -std::numeric_limits<Float8>::digits);
+  x += std::ldexp(SrcType{1.0}, -std::numeric_limits<IntermediateType>::digits);
+  auto rounded_x = static_cast<Float8>(x);
+  return static_cast<SrcType>(rounded_x);
+}
+
+// This test tries to capture mistakes in `float8_base::ConverFrom` where it is
+// implemented by a series of conversions. e.g. converting a double to a float
+// to a float8 introduces double-rounding which makes the final rounding step
+// unfaithful. Craft a variety of numbers which try to detect if this happens.
+TYPED_TEST(Float8Test, DoubleRound) {
+  using Float8 = TypeParam;
+
+  // We expect that our number results in rounding up to the number after 1.
+  // Incorrect rounding will result in 1.
+  const double expected =
+      1.0 + static_cast<double>(std::numeric_limits<Float8>::epsilon());
+
+  // Don't use long double on targets which don't support it.
+#if !defined(EIGEN_USE_GPU) && !defined(EIGEN_GPU_COMPILE_PHASE)
+  EXPECT_EQ((DoubleRoundHelper<long double, double, Float8>()), expected);
+  EXPECT_EQ((DoubleRoundHelper<long double, float, Float8>()), expected);
+#endif
+  EXPECT_EQ((DoubleRoundHelper<double, float, Float8>()), expected);
+}
+
 TEST(Float8Test, Float8E5m2_To_Float8E4m3) {
   // Saturation.
   float8_e5m2 max = std::numeric_limits<float8_e5m2>::max();
@@ -677,7 +711,7 @@ TYPED_TEST(Float8Test, CallTheConstOperator) {
   }
 }
 
-TEST(Float855m2Test, SmallCastToDenormal) {
+TEST(Float8E5m2Test, SmallCastToDenormal) {
   // Special edge-case where rounding to a normalized value would
   // normally round down, but rounding to a subnormal rounds up.
   float x = std::ldexp(1.3125, -15);