diff --git a/spring-cloud-sleuth-core/src/main/java/org/springframework/cloud/sleuth/instrument/web/client/TraceRequestHttpHeadersFilter.java b/spring-cloud-sleuth-core/src/main/java/org/springframework/cloud/sleuth/instrument/web/client/TraceRequestHttpHeadersFilter.java
index 079fd6428..4774b910c 100644
--- a/spring-cloud-sleuth-core/src/main/java/org/springframework/cloud/sleuth/instrument/web/client/TraceRequestHttpHeadersFilter.java
+++ b/spring-cloud-sleuth-core/src/main/java/org/springframework/cloud/sleuth/instrument/web/client/TraceRequestHttpHeadersFilter.java
@@ -15,8 +15,6 @@
  */
 package org.springframework.cloud.sleuth.instrument.web.client;
 
-import java.util.Collections;
-
 import brave.Span;
 import brave.Tracer;
 import brave.http.HttpClientHandler;
@@ -110,8 +108,7 @@ abstract class AbstractHttpHeadersFilter implements HttpHeadersFilter {
 	private static final Propagation.Setter<ServerHttpRequest.Builder, String> SETTER = new Propagation.Setter<ServerHttpRequest.Builder, String>() {
 		@Override
 		public void put(ServerHttpRequest.Builder carrier, String key, String value) {
-			carrier.headers(httpHeaders -> httpHeaders.replace(key,
-					Collections.singletonList(value)));
+			carrier.headers(httpHeaders -> httpHeaders.set(key, value));
 		}
 
 		@Override
diff --git a/spring-cloud-sleuth-core/src/test/java/org/springframework/cloud/sleuth/instrument/web/client/TraceRequestHttpHeadersFilterTests.java b/spring-cloud-sleuth-core/src/test/java/org/springframework/cloud/sleuth/instrument/web/client/TraceRequestHttpHeadersFilterTests.java
index 026f8ec7d..90eae741d 100644
--- a/spring-cloud-sleuth-core/src/test/java/org/springframework/cloud/sleuth/instrument/web/client/TraceRequestHttpHeadersFilterTests.java
+++ b/spring-cloud-sleuth-core/src/test/java/org/springframework/cloud/sleuth/instrument/web/client/TraceRequestHttpHeadersFilterTests.java
@@ -25,7 +25,7 @@ public class TraceRequestHttpHeadersFilterTests {
 	HttpTracing httpTracing = HttpTracing.newBuilder(this.tracing).build();
 
 	@Test
-	public void should_override_any_tracing_headers() {
+	public void should_override_span_tracing_headers() {
 		HttpHeadersFilter filter = TraceRequestHttpHeadersFilter.create(this.httpTracing);
 		HttpHeaders httpHeaders = new HttpHeaders();
 		httpHeaders.set("X-B3-TraceId", "52f112af7472aff0");
@@ -46,4 +46,22 @@ public class TraceRequestHttpHeadersFilterTests {
 				.isNotNull();
 	}
 
+	@Test
+	public void should_set_tracing_headers() {
+		HttpHeadersFilter filter = TraceRequestHttpHeadersFilter.create(this.httpTracing);
+		HttpHeaders httpHeaders = new HttpHeaders();
+		MockServerHttpRequest request = MockServerHttpRequest.post("foo/bar")
+				.headers(httpHeaders).build();
+		MockServerWebExchange exchange = MockServerWebExchange.builder(request).build();
+
+		HttpHeaders filteredHeaders = filter.filter(httpHeaders, exchange);
+
+		BDDAssertions.then(filteredHeaders.get("X-B3-TraceId")).isNotEmpty();
+		BDDAssertions.then(filteredHeaders.get("X-B3-SpanId")).isNotEmpty();
+		BDDAssertions
+				.then((Object) exchange
+						.getAttribute(TraceRequestHttpHeadersFilter.SPAN_ATTRIBUTE))
+				.isNotNull();
+	}
+
 }
\ No newline at end of file