diff --git a/libcxx/docs/ReleaseNotes.rst b/libcxx/docs/ReleaseNotes.rst
--- a/libcxx/docs/ReleaseNotes.rst
+++ b/libcxx/docs/ReleaseNotes.rst
@@ -79,13 +79,6 @@
   in namespace ``std``, it might be because one of your source files now needs to
   include one or more of the headers listed above.
 
-- The integer distributions ``binomial_distribution``, ``discrete_distribution``,
-  ``geometric_distribution``, ``negative_binomial_distribution``, ``poisson_distribution``,
-  and ``uniform_int_distribution`` now conform to the Standard by rejecting
-  template parameter types other than ``short``, ``int``, ``long``, ``long long``,
-  (as an extension) ``__int128_t``, and the unsigned versions thereof.
-  In particular, ``uniform_int_distribution<int8_t>`` is no longer supported.
-
 - The C++14 function ``std::quoted(const char*)`` is no longer supported in
   C++03 or C++11 modes.
 
diff --git a/libcxx/include/__random/binomial_distribution.h b/libcxx/include/__random/binomial_distribution.h
--- a/libcxx/include/__random/binomial_distribution.h
+++ b/libcxx/include/__random/binomial_distribution.h
@@ -24,10 +24,8 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-template<class _IntType = int>
-class _LIBCPP_TEMPLATE_VIS binomial_distribution
-{
-    static_assert(__libcpp_random_is_valid_inttype<_IntType>::value, "IntType must be an integer type larger than char");
+template <class _IntType = int>
+class _LIBCPP_TEMPLATE_VIS binomial_distribution {
 public:
     // types
     typedef _IntType result_type;
diff --git a/libcxx/include/__random/discrete_distribution.h b/libcxx/include/__random/discrete_distribution.h
--- a/libcxx/include/__random/discrete_distribution.h
+++ b/libcxx/include/__random/discrete_distribution.h
@@ -27,10 +27,8 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-template<class _IntType = int>
-class _LIBCPP_TEMPLATE_VIS discrete_distribution
-{
-    static_assert(__libcpp_random_is_valid_inttype<_IntType>::value, "IntType must be an integer type larger than char");
+template <class _IntType = int>
+class _LIBCPP_TEMPLATE_VIS discrete_distribution {
 public:
     // types
     typedef _IntType result_type;
diff --git a/libcxx/include/__random/geometric_distribution.h b/libcxx/include/__random/geometric_distribution.h
--- a/libcxx/include/__random/geometric_distribution.h
+++ b/libcxx/include/__random/geometric_distribution.h
@@ -10,7 +10,6 @@
 #define _LIBCPP___RANDOM_GEOMETRIC_DISTRIBUTION_H
 
 #include <__config>
-#include <__random/is_valid.h>
 #include <__random/negative_binomial_distribution.h>
 #include <iosfwd>
 #include <limits>
@@ -24,10 +23,8 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-template<class _IntType = int>
-class _LIBCPP_TEMPLATE_VIS geometric_distribution
-{
-    static_assert(__libcpp_random_is_valid_inttype<_IntType>::value, "IntType must be an integer type larger than char");
+template <class _IntType = int>
+class _LIBCPP_TEMPLATE_VIS geometric_distribution {
 public:
     // types
     typedef _IntType result_type;
diff --git a/libcxx/include/__random/is_valid.h b/libcxx/include/__random/is_valid.h
--- a/libcxx/include/__random/is_valid.h
+++ b/libcxx/include/__random/is_valid.h
@@ -18,27 +18,6 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-// [rand.req.genl]/1.5:
-// The effect of instantiating a template that has a template type parameter
-// named IntType is undefined unless the corresponding template argument is
-// cv-unqualified and is one of short, int, long, long long, unsigned short,
-// unsigned int, unsigned long, or unsigned long long.
-
-template<class> struct __libcpp_random_is_valid_inttype : false_type {};
-template<> struct __libcpp_random_is_valid_inttype<short> : true_type {};
-template<> struct __libcpp_random_is_valid_inttype<int> : true_type {};
-template<> struct __libcpp_random_is_valid_inttype<long> : true_type {};
-template<> struct __libcpp_random_is_valid_inttype<long long> : true_type {};
-template<> struct __libcpp_random_is_valid_inttype<unsigned short> : true_type {};
-template<> struct __libcpp_random_is_valid_inttype<unsigned int> : true_type {};
-template<> struct __libcpp_random_is_valid_inttype<unsigned long> : true_type {};
-template<> struct __libcpp_random_is_valid_inttype<unsigned long long> : true_type {};
-
-#ifndef _LIBCPP_HAS_NO_INT128
-template<> struct __libcpp_random_is_valid_inttype<__int128_t> : true_type {};
-template<> struct __libcpp_random_is_valid_inttype<__uint128_t> : true_type {};
-#endif // _LIBCPP_HAS_NO_INT128
-
 // [rand.req.urng]/3:
 // A class G meets the uniform random bit generator requirements if G models
 // uniform_random_bit_generator, invoke_result_t<G&> is an unsigned integer type,
diff --git a/libcxx/include/__random/negative_binomial_distribution.h b/libcxx/include/__random/negative_binomial_distribution.h
--- a/libcxx/include/__random/negative_binomial_distribution.h
+++ b/libcxx/include/__random/negative_binomial_distribution.h
@@ -26,10 +26,8 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-template<class _IntType = int>
-class _LIBCPP_TEMPLATE_VIS negative_binomial_distribution
-{
-    static_assert(__libcpp_random_is_valid_inttype<_IntType>::value, "IntType must be an integer type larger than char");
+template <class _IntType = int>
+class _LIBCPP_TEMPLATE_VIS negative_binomial_distribution {
 public:
     // types
     typedef _IntType result_type;
diff --git a/libcxx/include/__random/poisson_distribution.h b/libcxx/include/__random/poisson_distribution.h
--- a/libcxx/include/__random/poisson_distribution.h
+++ b/libcxx/include/__random/poisson_distribution.h
@@ -12,7 +12,6 @@
 #include <__config>
 #include <__random/clamp_to_integral.h>
 #include <__random/exponential_distribution.h>
-#include <__random/is_valid.h>
 #include <__random/normal_distribution.h>
 #include <__random/uniform_real_distribution.h>
 #include <cmath>
@@ -28,10 +27,8 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-template<class _IntType = int>
-class _LIBCPP_TEMPLATE_VIS poisson_distribution
-{
-    static_assert(__libcpp_random_is_valid_inttype<_IntType>::value, "IntType must be an integer type larger than char");
+template <class _IntType = int>
+class _LIBCPP_TEMPLATE_VIS poisson_distribution {
 public:
     // types
     typedef _IntType result_type;
diff --git a/libcxx/include/__random/uniform_int_distribution.h b/libcxx/include/__random/uniform_int_distribution.h
--- a/libcxx/include/__random/uniform_int_distribution.h
+++ b/libcxx/include/__random/uniform_int_distribution.h
@@ -156,10 +156,8 @@
     return _Sp;
 }
 
-template<class _IntType = int>
-class uniform_int_distribution
-{
-    static_assert(__libcpp_random_is_valid_inttype<_IntType>::value, "IntType must be an integer type larger than char");
+template <class _IntType = int> // __int128_t is also supported as an extension here
+class uniform_int_distribution {
 public:
     // types
     typedef _IntType result_type;
@@ -226,6 +224,14 @@
             {return !(__x == __y);}
 };
 
+template <class _Tp>
+struct __unsigned_equivalent : make_unsigned<_Tp> {};
+
+template <>
+struct __unsigned_equivalent<bool> {
+  using type = unsigned char;
+};
+
 template<class _IntType>
 template<class _URNG>
 typename uniform_int_distribution<_IntType>::result_type
@@ -233,8 +239,8 @@
 _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
 {
     static_assert(__libcpp_random_is_valid_urng<_URNG>::value, "");
-    typedef typename conditional<sizeof(result_type) <= sizeof(uint32_t), uint32_t,
-                                 typename make_unsigned<result_type>::type>::type _UIntType;
+    using _UIntType =
+        _If<sizeof(result_type) <= sizeof(uint32_t), uint32_t, typename __unsigned_equivalent<result_type>::type>;
     const _UIntType _Rp = _UIntType(__p.b()) - _UIntType(__p.a()) + _UIntType(1);
     if (_Rp == 1)
         return __p.a();
diff --git a/libcxx/test/libcxx/numerics/rand/rand.req.urng/valid_int_type.verify.cpp b/libcxx/test/libcxx/numerics/rand/rand.req.urng/valid_int_type.verify.cpp
deleted file mode 100644
--- a/libcxx/test/libcxx/numerics/rand/rand.req.urng/valid_int_type.verify.cpp
+++ /dev/null
@@ -1,51 +0,0 @@
-//===----------------------------------------------------------------------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-// <random>
-
-#include <random>
-
-void test()
-{
-  {
-    std::binomial_distribution<bool> baddist; //expected-error@*:* {{IntType must be an integer type larger than char}}
-    std::binomial_distribution<int> okdist;
-    (void)baddist;
-    (void)okdist;
-  }
-  {
-    std::discrete_distribution<bool> baddist; //expected-error@*:* {{IntType must be an integer type larger than char}}
-    std::discrete_distribution<int> okdist;
-    (void)baddist;
-    (void)okdist;
-  }
-  {
-    std::geometric_distribution<bool> baddist; //expected-error@*:* {{IntType must be an integer type larger than char}}
-    std::geometric_distribution<int> okdist;
-    (void)baddist;
-    (void)okdist;
-  }
-  {
-    std::negative_binomial_distribution<bool> baddist; //expected-error@*:* {{IntType must be an integer type larger than char}}
-    std::negative_binomial_distribution<int> okdist;
-    (void)baddist;
-    (void)okdist;
-  }
-  {
-    std::poisson_distribution<bool> baddist; //expected-error@*:* {{IntType must be an integer type larger than char}}
-    std::poisson_distribution<int> okdist;
-    (void)baddist;
-    (void)okdist;
-  }
-  {
-    std::uniform_int_distribution<bool> baddist; //expected-error@*:* {{IntType must be an integer type larger than char}}
-    std::uniform_int_distribution<int> okdist;
-    (void)baddist;
-    (void)okdist;
-  }
-}
diff --git a/libcxx/test/std/numerics/rand/rand.dis/rand.dist.uni/rand.dist.uni.int/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dis/rand.dist.uni/rand.dist.uni.int/eval.pass.cpp
--- a/libcxx/test/std/numerics/rand/rand.dis/rand.dist.uni/rand.dist.uni.int/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dis/rand.dist.uni/rand.dist.uni.int/eval.pass.cpp
@@ -16,9 +16,11 @@
 // template<class _URNG> result_type operator()(_URNG& g);
 
 #include <random>
+#include <algorithm>
 #include <cassert>
 #include <climits>
 #include <cstddef>
+#include <iterator>
 #include <limits>
 #include <numeric>
 #include <vector>
@@ -99,6 +101,25 @@
     test_statistics<ResultType, EngineType>(0, std::numeric_limits<ResultType>::max());
 }
 
+// Since the values should be uniformly distributed, and there's only two
+// values, we should have roughly half `false` and half `true`. That means we
+// can have a simple test for `bool`.
+template <class EngineType>
+void test_bool_statistics() {
+  EngineType gen;
+  std::uniform_int_distribution<bool> dist(false, true);
+  assert(dist.a() == false);
+  assert(dist.b() == true);
+  // We use 100x more values than non-bool tests to secure >99.9% confidence.
+  std::vector<bool> values(1000000);
+  for (auto i : values) {
+    i = dist(gen);
+  }
+
+  double average = std::accumulate(values.begin(), values.end(), 0.0) / values.size();
+  assert(0.49875 < average && average < 0.50125);
+}
+
 int main(int, char**)
 {
     test_statistics<int, std::minstd_rand0>();
@@ -113,16 +134,32 @@
     test_statistics<int, std::minstd_rand0>(-6, 106);
     test_statistics<int, std::minstd_rand>(5, 100);
 
+    test_statistics<char, std::minstd_rand0>();
+
+    test_statistics<signed char, std::minstd_rand0>();
     test_statistics<short, std::minstd_rand0>();
     test_statistics<int, std::minstd_rand0>();
     test_statistics<long, std::minstd_rand0>();
     test_statistics<long long, std::minstd_rand0>();
 
+    test_statistics<unsigned char, std::minstd_rand0>();
     test_statistics<unsigned short, std::minstd_rand0>();
     test_statistics<unsigned int, std::minstd_rand0>();
     test_statistics<unsigned long, std::minstd_rand0>();
     test_statistics<unsigned long long, std::minstd_rand0>();
 
+    test_bool_statistics<std::minstd_rand0>();
+    test_bool_statistics<std::minstd_rand>();
+    test_bool_statistics<std::mt19937>();
+    test_bool_statistics<std::mt19937_64>();
+    test_bool_statistics<std::ranlux24_base>();
+    test_bool_statistics<std::ranlux48_base>();
+    test_bool_statistics<std::ranlux24>();
+    test_bool_statistics<std::ranlux48>();
+    test_bool_statistics<std::knuth_b>();
+
+    test_statistics<char, std::minstd_rand0>(CHAR_MIN, CHAR_MAX);
+    test_statistics<signed char, std::minstd_rand0>(SCHAR_MIN, SCHAR_MAX);
     test_statistics<short, std::minstd_rand0>(SHRT_MIN, SHRT_MAX);
 
     // http://eel.is/c++draft/rand.req#genl-1.5