diff --git a/spring-web/src/main/java/org/springframework/web/filter/reactive/ServerWebExchangeContextFilter.java b/spring-web/src/main/java/org/springframework/web/filter/reactive/ServerWebExchangeContextFilter.java
index 08e42e27e3..7ff17b7246 100644
--- a/spring-web/src/main/java/org/springframework/web/filter/reactive/ServerWebExchangeContextFilter.java
+++ b/spring-web/src/main/java/org/springframework/web/filter/reactive/ServerWebExchangeContextFilter.java
@@ -1,5 +1,5 @@
 /*
- * Copyright 2002-2019 the original author or authors.
+ * Copyright 2002-2023 the original author or authors.
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
@@ -48,33 +48,35 @@ public class ServerWebExchangeContextFilter implements WebFilter {
 	@Override
 	public Mono<Void> filter(ServerWebExchange exchange, WebFilterChain chain) {
 		return chain.filter(exchange)
-				.contextWrite(cxt -> cxt.put(EXCHANGE_CONTEXT_ATTRIBUTE, exchange));
+				.contextWrite(context -> context.put(EXCHANGE_CONTEXT_ATTRIBUTE, exchange));
 	}
 
 
 	/**
-	 * Access the {@link ServerWebExchange} from the Reactor Context, if available,
-	 * which is if {@link ServerWebExchangeContextFilter} is configured for use
-	 * and the give context was obtained from a request processing chain.
-	 * @param context the context in which to access the exchange
-	 * @return the exchange
+	 * Access the {@link ServerWebExchange} from a Reactor {@link ContextView},
+	 * if available, which is generally the case when
+	 * {@link ServerWebExchangeContextFilter} is present in the filter chain.
+	 * @param contextView the contextView to get the exchange from
+	 * @return an {@link Optional} with the exchange if found
+	 * @since 6.0.6
 	 */
-	public static Optional<ServerWebExchange> getExchange(ContextView context) {
+	public static Optional<ServerWebExchange> getExchange(ContextView contextView) {
+		return contextView.getOrEmpty(EXCHANGE_CONTEXT_ATTRIBUTE);
+	}
+
+	/**
+	 * Access the {@link ServerWebExchange} from a Reactor {@link Context},
+	 * if available, which is generally the case when
+	 * {@link ServerWebExchangeContextFilter} is present in the filter chain.
+	 * @param context the context to get the exchange from
+	 * @return an {@link Optional} with the exchange if found
+	 * @deprecated in favor of using {@link #getExchange(ContextView)} which
+	 * accepts a {@link ContextView} instead of {@link Context}, reflecting the
+	 * fact that the {@code ContextView} is needed only for reading.
+	 */
+	@Deprecated(since = "6.0.6", forRemoval = true)
+	public static Optional<ServerWebExchange> get(Context context) {
 		return context.getOrEmpty(EXCHANGE_CONTEXT_ATTRIBUTE);
 	}
 
-
-	/**
-	 * Access the {@link ServerWebExchange} from the Reactor Context, if available,
-	 * which is if {@link ServerWebExchangeContextFilter} is configured for use
-	 * and the give context was obtained from a request processing chain.
-	 * @param context the context in which to access the exchange
-	 * @return the exchange
-	 * @deprecated use {@link #getExchange(ContextView)}
-	 */
-	@Deprecated(since = "6.0.6")
-	public static Optional<ServerWebExchange> get(Context context) {
-		return getExchange(context);
-	}
-
 }
diff --git a/spring-web/src/test/java/org/springframework/web/filter/reactive/ServerWebExchangeContextFilterTests.java b/spring-web/src/test/java/org/springframework/web/filter/reactive/ServerWebExchangeContextFilterTests.java
index 25f0edd7a4..196ce5f739 100644
--- a/spring-web/src/test/java/org/springframework/web/filter/reactive/ServerWebExchangeContextFilterTests.java
+++ b/spring-web/src/test/java/org/springframework/web/filter/reactive/ServerWebExchangeContextFilterTests.java
@@ -1,5 +1,5 @@
 /*
- * Copyright 2002-2020 the original author or authors.
+ * Copyright 2002-2023 the original author or authors.
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
@@ -22,7 +22,6 @@ import java.util.concurrent.atomic.AtomicReference;
 import org.junit.jupiter.api.Test;
 import reactor.core.publisher.Mono;
 
-import org.springframework.http.server.reactive.HttpHandler;
 import org.springframework.web.server.ServerWebExchange;
 import org.springframework.web.server.adapter.WebHttpHandlerBuilder;
 import org.springframework.web.testfixture.http.server.reactive.MockServerHttpRequest;
@@ -36,16 +35,16 @@ import static org.assertj.core.api.Assertions.assertThat;
  */
 class ServerWebExchangeContextFilterTests {
 
+
 	@Test
 	void extractServerWebExchangeFromContext() {
 		MyService service = new MyService();
 
-		HttpHandler httpHandler = WebHttpHandlerBuilder
+		WebHttpHandlerBuilder
 				.webHandler(exchange -> service.service().then())
 				.filter(new ServerWebExchangeContextFilter())
-				.build();
-
-		httpHandler.handle(MockServerHttpRequest.get("/path").build(), new MockServerHttpResponse())
+				.build()
+				.handle(MockServerHttpRequest.get("/path").build(), new MockServerHttpResponse())
 				.block(Duration.ofSeconds(5));
 
 		assertThat(service.getExchange()).isNotNull();
@@ -56,16 +55,16 @@ class ServerWebExchangeContextFilterTests {
 
 		private final AtomicReference<ServerWebExchange> exchangeRef = new AtomicReference<>();
 
-
 		public ServerWebExchange getExchange() {
 			return this.exchangeRef.get();
 		}
 
 		public Mono<String> service() {
-			return Mono.just("result").contextWrite(context -> {
-				ServerWebExchangeContextFilter.getExchange(context).ifPresent(exchangeRef::set);
-				return context;
-			});
+			return Mono.just("result")
+					.transformDeferredContextual((mono, contextView) -> {
+						ServerWebExchangeContextFilter.getExchange(contextView).ifPresent(exchangeRef::set);
+						return mono;
+					});
 		}
 	}