diff --git a/src/random.cpp b/src/random.cpp
index 3b7f7910b..3277c34d3 100644
--- a/src/random.cpp
+++ b/src/random.cpp
@@ -514,9 +514,11 @@ void GetRandBytes(unsigned char* buf, int num) noexcept { ProcRand(buf, num, RNG
 void GetStrongRandBytes(unsigned char* buf, int num) noexcept { ProcRand(buf, num, RNGLevel::SLOW); }
 void RandAddSeedSleep() { ProcRand(nullptr, 0, RNGLevel::SLEEP); }
 
+bool g_mock_deterministic_tests{false};
+
 uint64_t GetRand(uint64_t nMax) noexcept
 {
-    return FastRandomContext().randrange(nMax);
+    return FastRandomContext(g_mock_deterministic_tests).randrange(nMax);
 }
 
 int GetRandInt(int nMax) noexcept
diff --git a/src/test/bloom_tests.cpp b/src/test/bloom_tests.cpp
index c900bee19..f58dd20ef 100644
--- a/src/test/bloom_tests.cpp
+++ b/src/test/bloom_tests.cpp
@@ -461,6 +461,9 @@ static std::vector<unsigned char> RandomData()
 
 BOOST_AUTO_TEST_CASE(rolling_bloom)
 {
+    SeedInsecureRand(/* deterministic */ true);
+    g_mock_deterministic_tests = true;
+
     // last-100-entry, 1% false positive:
     CRollingBloomFilter rb1(100, 0.01);
 
@@ -485,12 +488,8 @@ BOOST_AUTO_TEST_CASE(rolling_bloom)
         if (rb1.contains(RandomData()))
             ++nHits;
     }
-    // Run test_bitcoin with --log_level=message to see BOOST_TEST_MESSAGEs:
-    BOOST_TEST_MESSAGE("RollingBloomFilter got " << nHits << " false positives (~100 expected)");
-
-    // Insanely unlikely to get a fp count outside this range:
-    BOOST_CHECK(nHits > 25);
-    BOOST_CHECK(nHits < 175);
+    // Expect about 100 hits
+    BOOST_CHECK_EQUAL(nHits, 75);
 
     BOOST_CHECK(rb1.contains(data[DATASIZE-1]));
     rb1.reset();
@@ -517,10 +516,8 @@ BOOST_AUTO_TEST_CASE(rolling_bloom)
         if (rb1.contains(data[i]))
             ++nHits;
     }
-    // Expect about 5 false positives, more than 100 means
-    // something is definitely broken.
-    BOOST_TEST_MESSAGE("RollingBloomFilter got " << nHits << " false positives (~5 expected)");
-    BOOST_CHECK(nHits < 100);
+    // Expect about 5 false positives
+    BOOST_CHECK_EQUAL(nHits, 6);
 
     // last-1000-entry, 0.01% false positive:
     CRollingBloomFilter rb2(1000, 0.001);
@@ -531,6 +528,7 @@ BOOST_AUTO_TEST_CASE(rolling_bloom)
     for (int i = 0; i < DATASIZE; i++) {
         BOOST_CHECK(rb2.contains(data[i]));
     }
+    g_mock_deterministic_tests = false;
 }
 
 BOOST_AUTO_TEST_SUITE_END()
diff --git a/src/test/random_tests.cpp b/src/test/random_tests.cpp
index 1057d0947..8194070ab 100644
--- a/src/test/random_tests.cpp
+++ b/src/test/random_tests.cpp
@@ -21,9 +21,14 @@ BOOST_AUTO_TEST_CASE(osrandom_tests)
 BOOST_AUTO_TEST_CASE(fastrandom_tests)
 {
     // Check that deterministic FastRandomContexts are deterministic
+    g_mock_deterministic_tests = true;
     FastRandomContext ctx1(true);
     FastRandomContext ctx2(true);
 
+    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(ctx1.rand32(), ctx2.rand32());
     BOOST_CHECK_EQUAL(ctx1.rand32(), ctx2.rand32());
     BOOST_CHECK_EQUAL(ctx1.rand64(), ctx2.rand64());
@@ -38,6 +43,11 @@ BOOST_AUTO_TEST_CASE(fastrandom_tests)
     BOOST_CHECK(ctx1.randbytes(50) == ctx2.randbytes(50));
 
     // Check that a nondeterministic ones are not
+    g_mock_deterministic_tests = false;
+    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});
+    }
     {
         FastRandomContext ctx3, ctx4;
         BOOST_CHECK(ctx3.rand64() != ctx4.rand64()); // extremely unlikely to be equal
diff --git a/src/test/test_bitcoin.h b/src/test/test_bitcoin.h
index 71520232a..4a0684568 100644
--- a/src/test/test_bitcoin.h
+++ b/src/test/test_bitcoin.h
@@ -35,6 +35,11 @@ std::ostream& operator<<(typename std::enable_if<std::is_enum<T>::value, std::os
  */
 extern FastRandomContext g_insecure_rand_ctx;
 
+/**
+ * Flag to make GetRand in random.h return the same number
+ */
+extern bool g_mock_deterministic_tests;
+
 static inline void SeedInsecureRand(bool deterministic = false)
 {
     g_insecure_rand_ctx = FastRandomContext(deterministic);