diff --git a/core/src/main/scala/org/http4s/jdkhttpclient/JdkHttpClient.scala b/core/src/main/scala/org/http4s/jdkhttpclient/JdkHttpClient.scala
index b32eb82b..61aa71d1 100644
--- a/core/src/main/scala/org/http4s/jdkhttpclient/JdkHttpClient.scala
+++ b/core/src/main/scala/org/http4s/jdkhttpclient/JdkHttpClient.scala
@@ -24,6 +24,7 @@ import fs2.Chunk
 import fs2.Stream
 import fs2.concurrent.SignallingRef
 import fs2.interop.flow
+import org.http4s.EmptyBody
 import org.http4s.Header
 import org.http4s.Headers
 import org.http4s.HttpVersion
@@ -63,16 +64,24 @@ object JdkHttpClient {
     def convertRequest(req: Request[F]): Resource[F, HttpRequest] =
       flow.toPublisher(req.body.chunks.map(_.toByteBuffer)).evalMap { publisher =>
         convertHttpVersionFromHttp4s[F](req.httpVersion).map { version =>
+          def consumeFully = (req.body ne EmptyBody) && (version match {
+            case HttpClient.Version.HTTP_1_1 => req.isChunked
+            case HttpClient.Version.HTTP_2 => req.contentLength.isEmpty
+          })
+
           val rb = HttpRequest.newBuilder
             .method(
               req.method.name,
-              if (req.isChunked)
+              if (consumeFully)
                 BodyPublishers.fromPublisher(publisher)
               else
                 req.contentLength match {
                   case Some(length) if length > 0L =>
                     BodyPublishers.fromPublisher(publisher, length)
-                  case _ => BodyPublishers.noBody
+                  case _ =>
+                    // If we dont do this, we might block finalization
+                    publisher.subscribe(DrainingSubscriber)
+                    BodyPublishers.noBody
                 }
             )
             .uri(URI.create(req.uri.renderString))
@@ -300,4 +309,12 @@ object JdkHttpClient {
       "via",
       "warning"
     ).map(CIString(_))
+
+  private object DrainingSubscriber extends Flow.Subscriber[ByteBuffer] {
+    override def onSubscribe(subscription: Flow.Subscription): Unit =
+      subscription.request(Long.MaxValue)
+    override def onNext(item: ByteBuffer): Unit = ()
+    override def onError(throwable: Throwable): Unit = ()
+    override def onComplete(): Unit = ()
+  }
 }