diff --git a/spring-web/src/main/java/org/springframework/web/client/RestTemplate.java b/spring-web/src/main/java/org/springframework/web/client/RestTemplate.java
index 9ccd5e4dd73..4e21a9f9e06 100644
--- a/spring-web/src/main/java/org/springframework/web/client/RestTemplate.java
+++ b/spring-web/src/main/java/org/springframework/web/client/RestTemplate.java
@@ -739,6 +739,9 @@ public class RestTemplate extends InterceptingHttpAccessor implements RestOperat
 			if (requestCallback != null) {
 				requestCallback.doWithRequest(request);
 			}
+			if ((method == HttpMethod.DELETE || method == HttpMethod.PUT) && request.getHeaders().getAccept().isEmpty()) {
+				request.getHeaders().add("Accept", "*/*");
+			}
 			response = request.execute();
 			handleResponse(url, method, response);
 			return (responseExtractor != null ? responseExtractor.extractData(response) : null);
diff --git a/spring-web/src/test/java/org/springframework/web/client/RestTemplateTests.java b/spring-web/src/test/java/org/springframework/web/client/RestTemplateTests.java
index fbe20803a06..f899e6802ae 100644
--- a/spring-web/src/test/java/org/springframework/web/client/RestTemplateTests.java
+++ b/spring-web/src/test/java/org/springframework/web/client/RestTemplateTests.java
@@ -25,8 +25,13 @@ import java.util.EnumSet;
 import java.util.HashMap;
 import java.util.List;
 import java.util.Map;
+import java.util.Map.Entry;
 import java.util.Set;
+import java.util.stream.Collectors;
 
+import okhttp3.mockwebserver.MockResponse;
+import okhttp3.mockwebserver.MockWebServer;
+import okhttp3.mockwebserver.RecordedRequest;
 import org.junit.jupiter.api.BeforeEach;
 import org.junit.jupiter.api.Test;
 
@@ -43,6 +48,7 @@ import org.springframework.http.client.ClientHttpRequestFactory;
 import org.springframework.http.client.ClientHttpRequestInitializer;
 import org.springframework.http.client.ClientHttpRequestInterceptor;
 import org.springframework.http.client.ClientHttpResponse;
+import org.springframework.http.client.SimpleClientHttpRequestFactory;
 import org.springframework.http.converter.GenericHttpMessageConverter;
 import org.springframework.http.converter.HttpMessageConverter;
 import org.springframework.util.StreamUtils;
@@ -486,6 +492,47 @@ public class RestTemplateTests {
 		verify(response).close();
 	}
 
+	@Test
+	public void headerAcceptAllOnPut() throws Exception {
+		MockWebServer server = new MockWebServer();
+		server.enqueue(new MockResponse().setResponseCode(500).setBody("internal server error"));
+		server.start();
+		template.setRequestFactory(new SimpleClientHttpRequestFactory());
+
+		template.put(server.url("/internal/server/error").uri(), null);
+
+		RecordedRequest request = server.takeRequest();
+		assertThat(request.getHeader("Accept")).isEqualTo("*/*");
+
+		server.shutdown();
+	}
+
+	@Test
+	public void keepGivenAcceptHeaderOnPut() throws Exception {
+		MockWebServer server = new MockWebServer();
+		server.enqueue(new MockResponse().setResponseCode(500).setBody("internal server error"));
+		server.start();
+
+		template.setRequestFactory(new SimpleClientHttpRequestFactory());
+		HttpHeaders headers = new HttpHeaders();
+		headers.setAccept(Collections.singletonList(MediaType.APPLICATION_JSON));
+		HttpEntity<String> entity = new HttpEntity<>(null, headers);
+		template.exchange(server.url("/internal/server/error").uri(), PUT, entity, Void.class);
+
+		RecordedRequest request = server.takeRequest();
+
+			final List<List<String>> accepts = request.getHeaders().toMultimap().entrySet().stream()
+				.filter(entry -> entry.getKey().equalsIgnoreCase("accept"))
+				.map(Entry::getValue)
+				.collect(Collectors.toList());
+
+		assertThat(accepts).hasSize(1);
+		assertThat(accepts.get(0)).hasSize(1);
+		assertThat(accepts.get(0).get(0)).isEqualTo("application/json");
+
+		server.shutdown();
+	}
+
 	@Test
 	public void patchForObject() throws Exception {
 		mockTextPlainHttpMessageConverter();
@@ -532,6 +579,21 @@ public class RestTemplateTests {
 		verify(response).close();
 	}
 
+	@Test
+	public void headerAcceptAllOnDelete() throws Exception {
+		MockWebServer server = new MockWebServer();
+		server.enqueue(new MockResponse().setResponseCode(500).setBody("internal server error"));
+		server.start();
+		template.setRequestFactory(new SimpleClientHttpRequestFactory());
+
+		template.delete(server.url("/internal/server/error").uri());
+
+		RecordedRequest request = server.takeRequest();
+		assertThat(request.getHeader("Accept")).isEqualTo("*/*");
+
+		server.shutdown();
+	}
+
 	@Test
 	public void optionsForAllow() throws Exception {
 		mockSentRequest(OPTIONS, "https://example.com");