diff --git a/driver-core/src/main/com/mongodb/internal/TimeoutContext.java b/driver-core/src/main/com/mongodb/internal/TimeoutContext.java
index 35ffedbb16f..2a886704cd9 100644
--- a/driver-core/src/main/com/mongodb/internal/TimeoutContext.java
+++ b/driver-core/src/main/com/mongodb/internal/TimeoutContext.java
@@ -192,7 +192,10 @@ public long getMaxAwaitTimeMS() {
 
     public void runMaxTimeMS(final LongConsumer onRemaining) {
         if (maxTimeSupplier != null) {
-            runWithFixedTimeout(maxTimeSupplier.get(), onRemaining);
+            long maxTimeMS = maxTimeSupplier.get();
+            if (maxTimeMS > 0) {
+                runMinTimeout(onRemaining, maxTimeMS);
+            }
             return;
         }
         if (timeout == null) {
@@ -209,6 +212,22 @@ public void runMaxTimeMS(final LongConsumer onRemaining) {
 
     }
 
+    private void runMinTimeout(final LongConsumer onRemaining, final long fixedMs) {
+        Timeout timeout = timeoutIncludingRoundTrip();
+        if (timeout != null) {
+            timeout.run(MILLISECONDS, () -> {
+                        onRemaining.accept(fixedMs);
+                    },
+                    (renamingMs) -> {
+                        onRemaining.accept(Math.min(renamingMs, fixedMs));
+                    }, () -> {
+                        throwMongoTimeoutException("The operation exceeded the timeout limit.");
+                    });
+        } else {
+            onRemaining.accept(fixedMs);
+        }
+    }
+
     private static void runWithFixedTimeout(final long ms, final LongConsumer onRemaining) {
         if (ms != 0) {
             onRemaining.accept(ms);
@@ -227,10 +246,14 @@ public void resetToDefaultMaxTime() {
      * <p>
      * NOTE: Suitable for static user-defined values only (i.e MaxAwaitTimeMS),
      * not for running timeouts that adjust dynamically (CSOT).
+     *
+     * If remaining CSOT timeout is less than this static timeout, then CSOT timeout will be used.
+     *
      */
     public void setMaxTimeOverride(final long maxTimeMS) {
         this.maxTimeSupplier = () -> maxTimeMS;
     }
+
     /**
      * Disable the maxTimeMS override. This way the maxTimeMS will not
      * be appended to the command in the {@link CommandMessage}.
diff --git a/driver-core/src/test/resources/unified-test-format/client-side-operation-timeout/tailable-awaitData.json b/driver-core/src/test/resources/unified-test-format/client-side-operation-timeout/tailable-awaitData.json
index d0fe950dd8e..a29e7b3a867 100644
--- a/driver-core/src/test/resources/unified-test-format/client-side-operation-timeout/tailable-awaitData.json
+++ b/driver-core/src/test/resources/unified-test-format/client-side-operation-timeout/tailable-awaitData.json
@@ -4,7 +4,8 @@
   "schemaVersion": "1.9",
   "runOnRequirements": [
     {
-      "minServerVersion": "4.4"
+      "minServerVersion": "4.4",
+      "serverless": "forbid"
     }
   ],
   "createEntities": [
@@ -419,6 +420,141 @@
           ]
         }
       ]
+    },
+    {
+      "description": "apply remaining timeoutMS if less than maxAwaitTimeMS",
+      "operations": [
+        {
+          "name": "failPoint",
+          "object": "testRunner",
+          "arguments": {
+            "client": "failPointClient",
+            "failPoint": {
+              "configureFailPoint": "failCommand",
+              "mode": {
+                "times": 1
+              },
+              "data": {
+                "failCommands": [
+                  "getMore"
+                ],
+                "blockConnection": true,
+                "blockTimeMS": 30
+              }
+            }
+          }
+        },
+        {
+          "name": "createFindCursor",
+          "object": "collection",
+          "arguments": {
+            "filter": {
+              "_id": 1
+            },
+            "cursorType": "tailableAwait",
+            "batchSize": 1,
+            "maxAwaitTimeMS": 100,
+            "timeoutMS": 200
+          },
+          "saveResultAsEntity": "tailableCursor"
+        },
+        {
+          "name": "iterateOnce",
+          "object": "tailableCursor"
+        },
+        {
+          "name": "iterateUntilDocumentOrError",
+          "object": "tailableCursor",
+          "expectError": {
+            "isTimeoutError": true
+          }
+        }
+      ],
+      "expectEvents": [
+        {
+          "client": "client",
+          "ignoreExtraEvents": true,
+          "events": [
+            {
+              "commandStartedEvent": {
+                "commandName": "find",
+                "databaseName": "test"
+              }
+            },
+            {
+              "commandStartedEvent": {
+                "commandName": "getMore",
+                "databaseName": "test",
+                "command": {
+                  "maxTimeMS": {
+                    "$$lte": 100
+                  }
+                }
+              }
+            },
+            {
+              "commandStartedEvent": {
+                "commandName": "getMore",
+                "databaseName": "test",
+                "command": {
+                  "maxTimeMS": {
+                    "$$lte": 70
+                  }
+                }
+              }
+            }
+          ]
+        }
+      ]
+    },
+    {
+      "description": "apply maxAwaitTimeMS if less than remaining timeout",
+      "operations": [
+        {
+          "name": "createFindCursor",
+          "object": "collection",
+          "arguments": {
+            "filter": {},
+            "cursorType": "tailableAwait",
+            "batchSize": 1,
+            "maxAwaitTimeMS": 100,
+            "timeoutMS": 200
+          },
+          "saveResultAsEntity": "tailableCursor"
+        },
+        {
+          "name": "iterateOnce",
+          "object": "tailableCursor"
+        },
+        {
+          "name": "iterateOnce",
+          "object": "tailableCursor"
+        }
+      ],
+      "expectEvents": [
+        {
+          "client": "client",
+          "events": [
+            {
+              "commandStartedEvent": {
+                "commandName": "find",
+                "databaseName": "test"
+              }
+            },
+            {
+              "commandStartedEvent": {
+                "commandName": "getMore",
+                "databaseName": "test",
+                "command": {
+                  "maxTimeMS": {
+                    "$$lte": 100
+                  }
+                }
+              }
+            }
+          ]
+        }
+      ]
     }
   ]
-}
+}
\ No newline at end of file
diff --git a/driver-sync/src/test/functional/com/mongodb/client/unified/UnifiedTestModifications.java b/driver-sync/src/test/functional/com/mongodb/client/unified/UnifiedTestModifications.java
index df9706b8dd7..31b8ebb3bdf 100644
--- a/driver-sync/src/test/functional/com/mongodb/client/unified/UnifiedTestModifications.java
+++ b/driver-sync/src/test/functional/com/mongodb/client/unified/UnifiedTestModifications.java
@@ -65,6 +65,10 @@ public static void applyCustomizations(final TestDef def) {
 
         // client-side-operation-timeout (CSOT)
 
+        def.skipNoncompliantReactive("No good way to fulfill tryNext() requirement with a Publisher<T>")
+                .directory("client-side-operation-timeout")
+                .test("timeoutMS behaves correctly for tailable awaitData cursors", "apply remaining timeoutMS if less than maxAwaitTimeMS");
+
         // TODO-JAVA-5712
 
         // collection-management