diff --git a/contrib/devtools/test_deterministic_coverage.sh b/contrib/devtools/test_deterministic_coverage.sh
--- a/contrib/devtools/test_deterministic_coverage.sh
+++ b/contrib/devtools/test_deterministic_coverage.sh
@@ -15,7 +15,6 @@
 # Disable tests known to cause non-deterministic behaviour and document the source or point of non-determinism.
 NON_DETERMINISTIC_TESTS=(
     "coinselector_tests/knapsack_solver_test"                 # coinselector_tests.cpp: if (equal_sets(setCoinsRet, setCoinsRet2))
-    "denialofservice_tests/DoS_mapOrphans"                    # denialofservice_tests.cpp: it = mapOrphanTransactions.lower_bound(InsecureRand256());
     "fs_tests/fsbridge_fstream"                               # deterministic test failure?
     "miner_tests/CreateNewBlock_validity"                     # validation.cpp: if (GetMainSignals().CallbacksPending() > 10)
     "scheduler_tests/manythreads"                             # scheduler.cpp: CScheduler::serviceQueue()
diff --git a/src/test/denialofservice_tests.cpp b/src/test/denialofservice_tests.cpp
--- a/src/test/denialofservice_tests.cpp
+++ b/src/test/denialofservice_tests.cpp
@@ -4,12 +4,14 @@
 
 // Unit tests for denial-of-service detection/prevention code
 
+#include <arith_uint256.h>
 #include <banman.h>
 #include <chain.h>
 #include <chainparams.h>
 #include <config.h>
 #include <net.h>
 #include <net_processing.h>
+#include <pubkey.h>
 #include <script/sign.h>
 #include <script/signingprovider.h>
 #include <script/standard.h>
@@ -348,9 +350,25 @@
     return it->second.tx;
 }
 
+static void MakeNewKeyWithFastRandomContext(CKey &key) {
+    std::vector<uint8_t> keydata;
+    keydata = g_insecure_rand_ctx.randbytes(32);
+    key.Set(keydata.data(), keydata.data() + keydata.size(),
+            /*fCompressedIn*/ true);
+    assert(key.IsValid());
+}
+
 BOOST_AUTO_TEST_CASE(DoS_mapOrphans) {
+    // This test had non-deterministic coverage due to
+    // randomly selected seeds.
+    // This seed is chosen so that all branches of the function
+    // ecdsa_signature_parse_der_lax are executed during this test.
+    // Specifically branches that run only when an ECDSA
+    // signature's R and S values have leading zeros.
+    g_insecure_rand_ctx = FastRandomContext(ArithToUint256(arith_uint256(33)));
+
     CKey key;
-    key.MakeNewKey(true);
+    MakeNewKeyWithFastRandomContext(key);
     FillableSigningProvider keystore;
     BOOST_CHECK(keystore.AddKey(key));