diff --git a/src/test/coins_tests.cpp b/src/test/coins_tests.cpp
index 27d8db8b9e3..21ee7e6bdf0 100644
--- a/src/test/coins_tests.cpp
+++ b/src/test/coins_tests.cpp
@@ -43,7 +43,7 @@ public:
             return false;
         }
         coin = it->second;
-        if (coin.IsSpent() && insecure_randrange(2) == 0) {
+        if (coin.IsSpent() && insecure_randbool() == 0) {
             // Randomly return false in case of an empty entry.
             return false;
         }
@@ -200,20 +200,20 @@ BOOST_AUTO_TEST_CASE(coins_cache_simulation_test)
 
         if (insecure_randrange(100) == 0) {
             // Every 100 iterations, flush an intermediate cache
-            if (stack.size() > 1 && insecure_randrange(2) == 0) {
+            if (stack.size() > 1 && insecure_randbool() == 0) {
                 unsigned int flushIndex = insecure_randrange(stack.size() - 1);
                 stack[flushIndex]->Flush();
             }
         }
         if (insecure_randrange(100) == 0) {
             // Every 100 iterations, change the cache stack.
-            if (stack.size() > 0 && insecure_randrange(2) == 0) {
+            if (stack.size() > 0 && insecure_randbool() == 0) {
                 //Remove the top cache
                 stack.back()->Flush();
                 delete stack.back();
                 stack.pop_back();
             }
-            if (stack.size() == 0 || (stack.size() < 4 && insecure_randrange(2))) {
+            if (stack.size() == 0 || (stack.size() < 4 && insecure_randbool())) {
                 //Add a new cache
                 CCoinsView* tip = &base;
                 if (stack.size() > 0) {
@@ -433,19 +433,19 @@ BOOST_AUTO_TEST_CASE(updatecoins_simulation_test)
 
         if (insecure_randrange(100) == 0) {
             // Every 100 iterations, flush an intermediate cache
-            if (stack.size() > 1 && insecure_randrange(2) == 0) {
+            if (stack.size() > 1 && insecure_randbool() == 0) {
                 unsigned int flushIndex = insecure_randrange(stack.size() - 1);
                 stack[flushIndex]->Flush();
             }
         }
         if (insecure_randrange(100) == 0) {
             // Every 100 iterations, change the cache stack.
-            if (stack.size() > 0 && insecure_randrange(2) == 0) {
+            if (stack.size() > 0 && insecure_randbool() == 0) {
                 stack.back()->Flush();
                 delete stack.back();
                 stack.pop_back();
             }
-            if (stack.size() == 0 || (stack.size() < 4 && insecure_randrange(2))) {
+            if (stack.size() == 0 || (stack.size() < 4 && insecure_randbool())) {
                 CCoinsView* tip = &base;
                 if (stack.size() > 0) {
                     tip = stack.back();
diff --git a/src/test/pmt_tests.cpp b/src/test/pmt_tests.cpp
index 32086ead5e8..40893741577 100644
--- a/src/test/pmt_tests.cpp
+++ b/src/test/pmt_tests.cpp
@@ -22,7 +22,7 @@ public:
     // flip one bit in one of the hashes - this should break the authentication
     void Damage() {
         unsigned int n = insecure_randrange(vHash.size());
-        int bit = insecure_randrange(256);
+        int bit = insecure_randbits(8);
         *(vHash[n].begin() + (bit>>3)) ^= 1<<(bit&7);
     }
 };
diff --git a/src/test/prevector_tests.cpp b/src/test/prevector_tests.cpp
index 674221e0093..5d9d1872682 100644
--- a/src/test/prevector_tests.cpp
+++ b/src/test/prevector_tests.cpp
@@ -209,10 +209,10 @@ BOOST_AUTO_TEST_CASE(PrevectorTestInt)
                 test.resize(new_size);
             }
             if (insecure_randbits(3) == 3) {
-                test.insert(insecure_randrange(test.size() + 1), 1 + insecure_randrange(2), insecure_rand());
+                test.insert(insecure_randrange(test.size() + 1), 1 + insecure_randbool(), insecure_rand());
             }
             if (insecure_randbits(3) == 4) {
-                int del = std::min<int>(test.size(), 1 + (insecure_randrange(2)));
+                int del = std::min<int>(test.size(), 1 + (insecure_randbool()));
                 int beg = insecure_randrange(test.size() + 1 - del);
                 test.erase(beg, beg + del);
             }
@@ -224,19 +224,19 @@ BOOST_AUTO_TEST_CASE(PrevectorTestInt)
             }
             if (insecure_randbits(5) == 7) {
                 int values[4];
-                int num = 1 + (insecure_randrange(4));
+                int num = 1 + (insecure_randbits(2));
                 for (int k = 0; k < num; k++) {
                     values[k] = insecure_rand();
                 }
                 test.insert_range(insecure_randrange(test.size() + 1), values, values + num);
             }
             if (insecure_randbits(5) == 8) {
-                int del = std::min<int>(test.size(), 1 + (insecure_randrange(4)));
+                int del = std::min<int>(test.size(), 1 + (insecure_randbits(2)));
                 int beg = insecure_randrange(test.size() + 1 - del);
                 test.erase(beg, beg + del);
             }
             if (insecure_randbits(5) == 9) {
-                test.reserve(insecure_randrange(32));
+                test.reserve(insecure_randbits(5));
             }
             if (insecure_randbits(6) == 10) {
                 test.shrink_to_fit();
@@ -248,7 +248,7 @@ BOOST_AUTO_TEST_CASE(PrevectorTestInt)
                 test.clear();
             }
             if (insecure_randbits(9) == 12) {
-                test.assign(insecure_randrange(32), insecure_rand());
+                test.assign(insecure_randbits(5), insecure_rand());
             }
             if (insecure_randbits(3) == 3) {
                 test.swap();
diff --git a/src/test/sighash_tests.cpp b/src/test/sighash_tests.cpp
index 805c09c1a41..b8d6bdd730d 100644
--- a/src/test/sighash_tests.cpp
+++ b/src/test/sighash_tests.cpp
@@ -98,16 +98,16 @@ void static RandomTransaction(CMutableTransaction &tx, bool fSingle) {
     tx.nVersion = insecure_rand();
     tx.vin.clear();
     tx.vout.clear();
-    tx.nLockTime = (insecure_randrange(2)) ? insecure_rand() : 0;
-    int ins = (insecure_randrange(4)) + 1;
-    int outs = fSingle ? ins : (insecure_randrange(4)) + 1;
+    tx.nLockTime = (insecure_randbool()) ? insecure_rand() : 0;
+    int ins = (insecure_randbits(2)) + 1;
+    int outs = fSingle ? ins : (insecure_randbits(2)) + 1;
     for (int in = 0; in < ins; in++) {
         tx.vin.push_back(CTxIn());
         CTxIn &txin = tx.vin.back();
         txin.prevout.hash = insecure_rand256();
-        txin.prevout.n = insecure_randrange(4);
+        txin.prevout.n = insecure_randbits(2);
         RandomScript(txin.scriptSig);
-        txin.nSequence = (insecure_randrange(2)) ? insecure_rand() : (unsigned int)-1;
+        txin.nSequence = (insecure_randbool()) ? insecure_rand() : (unsigned int)-1;
     }
     for (int out = 0; out < outs; out++) {
         tx.vout.push_back(CTxOut());