diff --git a/src/random.cpp b/src/random.cpp
index 5b8782d1c..9c9a35709 100644
--- a/src/random.cpp
+++ b/src/random.cpp
@@ -14,16 +14,14 @@
 #include <wincrypt.h>
 #endif
 #include <logging.h>  // for LogPrintf()
+#include <randomenv.h>
+#include <support/allocators/secure.h>
 #include <sync.h>     // for Mutex
 #include <util/time.h> // for GetTimeMicros()
 
 #include <stdlib.h>
 #include <thread>
 
-#include <randomenv.h>
-
-#include <support/allocators/secure.h>
-
 #ifndef WIN32
 #include <fcntl.h>
 #include <sys/time.h>
@@ -590,16 +588,6 @@ uint64_t GetRand(uint64_t nMax) noexcept
     return FastRandomContext(g_mock_deterministic_tests).randrange(nMax);
 }
 
-std::chrono::microseconds GetRandMicros(std::chrono::microseconds duration_max) noexcept
-{
-    return std::chrono::microseconds{GetRand(duration_max.count())};
-}
-
-std::chrono::milliseconds GetRandMillis(std::chrono::milliseconds duration_max) noexcept
-{
-    return std::chrono::milliseconds{GetRand(duration_max.count())};
-}
-
 int GetRandInt(int nMax) noexcept
 {
     return GetRand(nMax);
diff --git a/src/random.h b/src/random.h
index 690125079..0c6dc2498 100644
--- a/src/random.h
+++ b/src/random.h
@@ -67,9 +67,21 @@
  * Thread-safe.
  */
 void GetRandBytes(unsigned char* buf, int num) noexcept;
+/** Generate a uniform random integer in the range [0..range). Precondition: range > 0 */
 uint64_t GetRand(uint64_t nMax) noexcept;
-std::chrono::microseconds GetRandMicros(std::chrono::microseconds duration_max) noexcept;
-std::chrono::milliseconds GetRandMillis(std::chrono::milliseconds duration_max) noexcept;
+/** Generate a uniform random duration in the range [0..max). Precondition: max.count() > 0 */
+template <typename D>
+D GetRandomDuration(typename std::common_type<D>::type max) noexcept
+// Having the compiler infer the template argument from the function argument
+// is dangerous, because the desired return value generally has a different
+// type than the function argument. So std::common_type is used to force the
+// call site to specify the type of the return value.
+{
+    assert(max.count() > 0);
+    return D{GetRand(max.count())};
+};
+constexpr auto GetRandMicros = GetRandomDuration<std::chrono::microseconds>;
+constexpr auto GetRandMillis = GetRandomDuration<std::chrono::milliseconds>;
 int GetRandInt(int nMax) noexcept;
 uint256 GetRandHash() noexcept;
 
diff --git a/src/test/random_tests.cpp b/src/test/random_tests.cpp
index d1f60e897..978a7bee4 100644
--- a/src/test/random_tests.cpp
+++ b/src/test/random_tests.cpp
@@ -28,6 +28,8 @@ BOOST_AUTO_TEST_CASE(fastrandom_tests)
     for (int i = 10; i > 0; --i) {
         BOOST_CHECK_EQUAL(GetRand(std::numeric_limits<uint64_t>::max()), uint64_t{10393729187455219830U});
         BOOST_CHECK_EQUAL(GetRandInt(std::numeric_limits<int>::max()), int{769702006});
+        BOOST_CHECK_EQUAL(GetRandMicros(std::chrono::hours{1}).count(), 2917185654);
+        BOOST_CHECK_EQUAL(GetRandMillis(std::chrono::hours{1}).count(), 2144374);
     }
     BOOST_CHECK_EQUAL(ctx1.rand32(), ctx2.rand32());
     BOOST_CHECK_EQUAL(ctx1.rand32(), ctx2.rand32());
@@ -47,6 +49,8 @@ BOOST_AUTO_TEST_CASE(fastrandom_tests)
     for (int i = 10; i > 0; --i) {
         BOOST_CHECK(GetRand(std::numeric_limits<uint64_t>::max()) != uint64_t{10393729187455219830U});
         BOOST_CHECK(GetRandInt(std::numeric_limits<int>::max()) != int{769702006});
+        BOOST_CHECK(GetRandMicros(std::chrono::hours{1}) != std::chrono::microseconds{2917185654});
+        BOOST_CHECK(GetRandMillis(std::chrono::hours{1}) != std::chrono::milliseconds{2144374});
     }
     {
         FastRandomContext ctx3, ctx4;
@@ -87,7 +91,7 @@ BOOST_AUTO_TEST_CASE(stdrandom_test)
         BOOST_CHECK(x >= 3);
         BOOST_CHECK(x <= 9);
 
-        std::vector<int> test{1,2,3,4,5,6,7,8,9,10};
+        std::vector<int> test{1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
         std::shuffle(test.begin(), test.end(), ctx);
         for (int j = 1; j <= 10; ++j) {
             BOOST_CHECK(std::find(test.begin(), test.end(), j) != test.end());
@@ -97,7 +101,6 @@ BOOST_AUTO_TEST_CASE(stdrandom_test)
             BOOST_CHECK(std::find(test.begin(), test.end(), j) != test.end());
         }
     }
-
 }
 
 /** Test that Shuffle reaches every permutation with equal probability. */