diff --git a/src/random.h b/src/random.h
--- a/src/random.h
+++ b/src/random.h
@@ -70,11 +70,27 @@
  * Thread-safe.
  */
 void GetRandBytes(uint8_t *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/random.cpp b/src/random.cpp
--- a/src/random.cpp
+++ b/src/random.cpp
@@ -642,16 +642,6 @@
     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/test/random_tests.cpp b/src/test/random_tests.cpp
--- a/src/test/random_tests.cpp
+++ b/src/test/random_tests.cpp
@@ -28,6 +28,10 @@
                           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());
@@ -49,6 +53,10 @@
                     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;