diff --git a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/FunctionAroundWrapper.java b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/FunctionAroundWrapper.java
index 92a364dad..bcf6c1cec 100644
--- a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/FunctionAroundWrapper.java
+++ b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/FunctionAroundWrapper.java
@@ -40,8 +40,7 @@ public abstract class FunctionAroundWrapper implements BiFunction<Object, Functi
 		String functionalTracingEnabledStr = System.getProperty("spring.sleuth.function.enabled");
 		boolean functionalTracingEnabled = StringUtils.hasText(functionalTracingEnabledStr)
 				? Boolean.parseBoolean(functionalTracingEnabledStr) : true;
-		if (functionalTracingEnabled && !targetFunction.isInputTypePublisher() &&
-				input instanceof Message && !FunctionTypeUtils.isCollectionOfMessage(targetFunction.getOutputType())) {
+		if (functionalTracingEnabled && input instanceof Message) {
 			boolean isSkipOutputConversion = targetFunction.isSkipOutputConversion();
 			targetFunction.setSkipOutputConversion(true);
 			try {
diff --git a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/SimpleFunctionRegistry.java b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/SimpleFunctionRegistry.java
index fe538ac30..a83d6e4b8 100644
--- a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/SimpleFunctionRegistry.java
+++ b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/SimpleFunctionRegistry.java
@@ -272,7 +272,8 @@ public class SimpleFunctionRegistry implements FunctionRegistry, FunctionInspect
 	 */
 	private FunctionInvocationWrapper wrapInAroundAdviceIfNecessary(FunctionInvocationWrapper function) {
 		FunctionInvocationWrapper wrappedFunction = function;
-		if (function != null && this.functionAroundWrapper != null) {
+		if (function != null && this.functionAroundWrapper != null && !function.isSupplier()
+				&& !function.isInputTypePublisher() && !function.isOutputTypePublisher() && !FunctionTypeUtils.isCollectionOfMessage(function.getOutputType())) {
 			wrappedFunction = new FunctionInvocationWrapper(function) {
 				@Override
 				Object doApply(Object input) {