diff --git a/mcp-core/src/main/java/io/modelcontextprotocol/client/McpClient.java b/mcp-core/src/main/java/io/modelcontextprotocol/client/McpClient.java
index 1af4eea..328566a 100644
--- a/mcp-core/src/main/java/io/modelcontextprotocol/client/McpClient.java
+++ b/mcp-core/src/main/java/io/modelcontextprotocol/client/McpClient.java
@@ -494,9 +494,10 @@ public interface McpClient {
 		 * calling any client operation. This allows to extract thread-locals and hand
 		 * them over to the underlying transport.
 		 * <p>
-		 * There is no direct equivalent in {@link AsyncSpec}. To achieve the same result,
-		 * append {@code contextWrite(McpTransportContext.KEY, context)} to any
-		 * {@link McpAsyncClient} call.
+		 * The supplier is invoked at subscription time, on the calling thread, and the
+		 * resulting context is visible to the transport for every leg of the operation,
+		 * including connections opened on other threads, such as the SSE stream started
+		 * during initialization.
 		 * @param contextProvider A supplier to create a context
 		 * @return This builder for method chaining
 		 */
@@ -580,6 +581,21 @@ public interface McpClient {
 	 * <li>Change notification handlers for tools, resources, and prompts
 	 * <li>Custom message sampling logic
 	 * </ul>
+	 *
+	 * <p>
+	 * Unlike {@link SyncSpec}, this specification has no
+	 * {@code transportContextProvider}. This is deliberate: in a reactive pipeline the
+	 * caller owns the Reactor context, and whatever the transport needs, such as an
+	 * {@link McpTransportContext}, can be written into it directly. Write it once where
+	 * the reactive chain starts, rather than at every call site, and every
+	 * {@link McpAsyncClient} call downstream inherits it, including the connections
+	 * opened during initialization: <pre>{@code
+	 * chain.filter(exchange)
+	 *     .contextWrite(ctx -> ctx.put(McpTransportContext.KEY, context));
+	 * }</pre> To bridge thread-locals into the chain, use Reactor's context propagation
+	 * support.
+	 *
+	 * @see SyncSpec#transportContextProvider(Supplier)
 	 */
 	class AsyncSpec {
 
diff --git a/mcp-core/src/main/java/io/modelcontextprotocol/client/transport/customizer/McpAsyncHttpClientRequestCustomizer.java b/mcp-core/src/main/java/io/modelcontextprotocol/client/transport/customizer/McpAsyncHttpClientRequestCustomizer.java
index 756b39c..f2951d8 100644
--- a/mcp-core/src/main/java/io/modelcontextprotocol/client/transport/customizer/McpAsyncHttpClientRequestCustomizer.java
+++ b/mcp-core/src/main/java/io/modelcontextprotocol/client/transport/customizer/McpAsyncHttpClientRequestCustomizer.java
@@ -7,18 +7,26 @@ package io.modelcontextprotocol.client.transport.customizer;
 import java.net.URI;
 import java.net.http.HttpRequest;
 
+import io.modelcontextprotocol.client.McpClient.SyncSpec;
+import io.modelcontextprotocol.common.McpTransportContext;
 import org.reactivestreams.Publisher;
 import reactor.core.publisher.Mono;
 import reactor.core.scheduler.Schedulers;
 import reactor.util.annotation.Nullable;
 
-import io.modelcontextprotocol.common.McpTransportContext;
-
 /**
  * Customize {@link HttpRequest.Builder} before executing the request, in either SSE or
  * Streamable HTTP transport.
  * <p>
  * When used in a non-blocking context, implementations MUST be non-blocking.
+ * <p>
+ * The {@link McpTransportContext} handed to {@code customize} is read from the Reactor
+ * context, under {@link McpTransportContext#KEY}, and is
+ * {@link McpTransportContext#EMPTY} when the caller wrote nothing there. Write it once
+ * where the reactive chain starts, with
+ * {@code contextWrite(ctx -> ctx.put(McpTransportContext.KEY, context))}, rather than at
+ * every call site. With a synchronous client, configure
+ * {@link SyncSpec#transportContextProvider} instead.
  *
  * @author Daniel Garnier-Moiroux
  */
diff --git a/mcp-core/src/main/java/io/modelcontextprotocol/common/McpTransportContext.java b/mcp-core/src/main/java/io/modelcontextprotocol/common/McpTransportContext.java
index 46a2ccf..4691c13 100644
--- a/mcp-core/src/main/java/io/modelcontextprotocol/common/McpTransportContext.java
+++ b/mcp-core/src/main/java/io/modelcontextprotocol/common/McpTransportContext.java
@@ -11,13 +11,28 @@ import java.util.Map;
  * Context associated with the transport layer. It allows to add transport-level metadata
  * for use further down the line. Specifically, it can be beneficial to extract HTTP
  * request metadata for use in MCP feature implementations.
+ * <p>
+ * The context travels in the Reactor context, under {@link #KEY}. On the server side, the
+ * transports populate it from the incoming request. On the client side, writing it is the
+ * caller's responsibility:
+ * <ul>
+ * <li>with a synchronous client, configure
+ * {@code McpClient.SyncSpec#transportContextProvider(Supplier)}, which is invoked on the
+ * calling thread before every operation;
+ * <li>with an asynchronous client, write it into the Reactor context once, where the
+ * reactive chain starts, using
+ * {@code contextWrite(ctx -> ctx.put(McpTransportContext.KEY, context))}. Every client
+ * call downstream inherits it, so there is no need to repeat it at each call site.
+ * </ul>
  *
  * @author Dariusz Jędrzejczyk
  */
 public interface McpTransportContext {
 
 	/**
-	 * Key for use in Reactor Context to transport the context to user land.
+	 * Key for use in Reactor Context to transport the context to user land. Write the
+	 * context under this key to make it visible to the transport, for example
+	 * {@code contextWrite(ctx -> ctx.put(McpTransportContext.KEY, context))}.
 	 */
 	String KEY = "MCP_TRANSPORT_CONTEXT";