diff --git a/src/random.cpp b/src/random.cpp
index b408b1e13e..27d8367de4 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>
@@ -587,16 +585,6 @@ 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 690125079b..0c6dc24983 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;