diff --git a/spring-web/src/main/java/org/springframework/web/server/MethodNotAllowedException.java b/spring-web/src/main/java/org/springframework/web/server/MethodNotAllowedException.java
index 40cf7d46607..e6e78dd8836 100644
--- a/spring-web/src/main/java/org/springframework/web/server/MethodNotAllowedException.java
+++ b/spring-web/src/main/java/org/springframework/web/server/MethodNotAllowedException.java
@@ -18,7 +18,7 @@ package org.springframework.web.server;
 
 import java.util.Collection;
 import java.util.Collections;
-import java.util.HashSet;
+import java.util.LinkedHashSet;
 import java.util.Map;
 import java.util.Set;
 
@@ -54,7 +54,7 @@ public class MethodNotAllowedException extends ResponseStatusException {
 			supportedMethods = Collections.emptySet();
 		}
 		this.method = method;
-		this.httpMethods = Collections.unmodifiableSet(new HashSet<>(supportedMethods));
+		this.httpMethods = Collections.unmodifiableSet(new LinkedHashSet<>(supportedMethods));
 	}
 
 
diff --git a/spring-webmvc/src/main/java/org/springframework/web/servlet/mvc/annotation/ResponseStatusExceptionResolver.java b/spring-webmvc/src/main/java/org/springframework/web/servlet/mvc/annotation/ResponseStatusExceptionResolver.java
index 5d8d40a5e3c..63873d01ff6 100644
--- a/spring-webmvc/src/main/java/org/springframework/web/servlet/mvc/annotation/ResponseStatusExceptionResolver.java
+++ b/spring-webmvc/src/main/java/org/springframework/web/servlet/mvc/annotation/ResponseStatusExceptionResolver.java
@@ -130,11 +130,8 @@ public class ResponseStatusExceptionResolver extends AbstractHandlerExceptionRes
 	protected ModelAndView resolveResponseStatusException(ResponseStatusException ex,
 			HttpServletRequest request, HttpServletResponse response, @Nullable Object handler) throws Exception {
 
-		ex.getResponseHeaders().forEach((name, values) -> {
-			if (response.getHeader(name) == null) {
-				values.forEach(value -> response.addHeader(name, value));
-			}
-		});
+		ex.getResponseHeaders().forEach((name, values) ->
+				values.forEach(value -> response.addHeader(name, value)));
 
 		int statusCode = ex.getStatus().value();
 		String reason = ex.getReason();