diff --git a/oemcrypto/test/oec_session_util.cpp b/oemcrypto/test/oec_session_util.cpp
index 6af0136..243c798 100644
--- a/oemcrypto/test/oec_session_util.cpp
+++ b/oemcrypto/test/oec_session_util.cpp
@@ -502,9 +502,13 @@ void LicenseRoundTrip::FillAndVerifyCoreRequest(
       oemcrypto_core_message::deserialize::CoreLicenseRequestFromMessage(
           core_message_string, &core_request_));
   EXPECT_EQ(global_features.api_version, core_request_.api_major_version);
-  // If we are testing the latest OEMCrypto version, make sure it is built with
-  // the latest ODK version, too:
-  if (global_features.api_version == ODK_MAJOR_VERSION) {
+  if (global_features.api_version == 16) {
+    // We support either 16.3 or 16.4 for OEMCrypto 16.
+    EXPECT_LE(3, core_request_.api_minor_version);
+    EXPECT_GE(4, core_request_.api_minor_version);
+  } else if (global_features.api_version == ODK_MAJOR_VERSION) {
+    // If we are testing the latest OEMCrypto version, make sure it is built
+    // with the latest ODK version, too:
     EXPECT_EQ(ODK_MINOR_VERSION, core_request_.api_minor_version);
   }
   if (expect_request_has_correct_nonce_) {