diff --git a/spring-web/src/main/java/org/springframework/http/client/SimpleBufferingClientHttpRequest.java b/spring-web/src/main/java/org/springframework/http/client/SimpleBufferingClientHttpRequest.java
index 52c3eb60e81eac0039f8613a85fdc28613647b14..394a83076354e186ffdd63a48a5e23144a6258fd 100644
--- a/spring-web/src/main/java/org/springframework/http/client/SimpleBufferingClientHttpRequest.java
+++ b/spring-web/src/main/java/org/springframework/http/client/SimpleBufferingClientHttpRequest.java
@@ -91,6 +91,14 @@ final class SimpleBufferingClientHttpRequest extends AbstractBufferingClientHttp
 	 * @param headers the headers to add
 	 */
 	static void addHeaders(HttpURLConnection connection, HttpHeaders headers) {
+		String method = connection.getRequestMethod();
+		if (method.equals("PUT") || method.equals("DELETE")) {
+			if (!StringUtils.hasText(headers.getFirst(HttpHeaders.ACCEPT))) {
+				// Avoid "text/html, image/gif, image/jpeg, *; q=.2, */*; q=.2"
+				// from HttpUrlConnection which prevents JSON error response details.
+				headers.set(HttpHeaders.ACCEPT, "*/*");
+			}
+		}
 		headers.forEach((headerName, headerValues) -> {
 			if (HttpHeaders.COOKIE.equalsIgnoreCase(headerName)) {  // RFC 6265
 				String headerValue = StringUtils.collectionToDelimitedString(headerValues, "; ");
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 4e21a9f9e06174dbb8cf63974e156411b83e8eb7..9ccd5e4dd7317c691ac7377ab304bd8aa704bebc 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
@@ -739,9 +739,6 @@ 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/http/client/SimpleClientHttpRequestFactoryTests.java b/spring-web/src/test/java/org/springframework/http/client/SimpleClientHttpRequestFactoryTests.java
index f698b01728b0b76c8e0009913d7a841ecb0f8d6e..df8f9a58893ff06412309670e0f84c331cf8c2f7 100644
--- a/spring-web/src/test/java/org/springframework/http/client/SimpleClientHttpRequestFactoryTests.java
+++ b/spring-web/src/test/java/org/springframework/http/client/SimpleClientHttpRequestFactoryTests.java
@@ -22,6 +22,7 @@ import org.junit.jupiter.api.Test;
 
 import org.springframework.http.HttpHeaders;
 
+import static org.mockito.BDDMockito.given;
 import static org.mockito.Mockito.mock;
 import static org.mockito.Mockito.times;
 import static org.mockito.Mockito.verify;
@@ -31,9 +32,11 @@ import static org.mockito.Mockito.verify;
  */
 public class SimpleClientHttpRequestFactoryTests {
 
-	@Test  // SPR-13225
+
+	@Test // SPR-13225
 	public void headerWithNullValue() {
 		HttpURLConnection urlConnection = mock(HttpURLConnection.class);
+		given(urlConnection.getRequestMethod()).willReturn("GET");
 		HttpHeaders headers = new HttpHeaders();
 		headers.set("foo", null);
 		SimpleBufferingClientHttpRequest.addHeaders(urlConnection, headers);
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 f899e6802ae4ba31231b970636eb7aa5b57f8366..3877572704d447f337daa500047a23978c6af0b5 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
@@ -492,45 +492,47 @@ public class RestTemplateTests {
 		verify(response).close();
 	}
 
-	@Test
+	@Test // gh-23740
 	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();
+		try {
+			template.setRequestFactory(new SimpleClientHttpRequestFactory());
+			template.put(server.url("/internal/server/error").uri(), null);
+			assertThat(server.takeRequest().getHeader("Accept")).isEqualTo("*/*");
+		}
+		finally {
+			server.shutdown();
+		}
 	}
 
-	@Test
+	@Test // gh-23740
 	public void keepGivenAcceptHeaderOnPut() throws Exception {
 		MockWebServer server = new MockWebServer();
 		server.enqueue(new MockResponse().setResponseCode(500).setBody("internal server error"));
 		server.start();
+		try {
+			HttpHeaders headers = new HttpHeaders();
+			headers.setAccept(Collections.singletonList(MediaType.APPLICATION_JSON));
+			HttpEntity<String> entity = new HttpEntity<>(null, headers);
+			template.setRequestFactory(new SimpleClientHttpRequestFactory());
+			template.exchange(server.url("/internal/server/error").uri(), PUT, entity, Void.class);
 
-		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();
+			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());
+					.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();
+			assertThat(accepts).hasSize(1);
+			assertThat(accepts.get(0)).hasSize(1);
+			assertThat(accepts.get(0).get(0)).isEqualTo("application/json");
+		}
+		finally {
+			server.shutdown();
+		}
 	}
 
 	@Test
@@ -579,19 +581,19 @@ public class RestTemplateTests {
 		verify(response).close();
 	}
 
-	@Test
+	@Test // gh-23740
 	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();
+		try {
+			template.setRequestFactory(new SimpleClientHttpRequestFactory());
+			template.delete(server.url("/internal/server/error").uri());
+			assertThat(server.takeRequest().getHeader("Accept")).isEqualTo("*/*");
+		}
+		finally {
+			server.shutdown();
+		}
 	}
 
 	@Test