diff --git a/nginx.tmpl b/nginx.tmpl
index c16b477..e8e36ac 100644
--- a/nginx.tmpl
+++ b/nginx.tmpl
@@ -284,9 +284,18 @@ server {
 
 	location / {
 	{{ if (hasPrefix "www." $host) }}
-		return 301 https://{{ trimPrefix "www." $host }}$request_uri;
-	{{ else }}
+	    # Redirect www. to non-www.
+		{{ $trimmedHost :=  trimPrefix "www." $host }}
+		{{ if eq $external_https_port "443" }}
+			return 301 https://{{ $trimmedHost }}$request_uri;
+		{{ else }}
+			return 301 https://{{ $trimmedHost }}:{{ $external_https_port }}$request_uri;
+		{{ end }}
+	{{ end }}
+	{{ if eq $external_https_port "443" }}
 		return 301 https://$host$request_uri;
+	{{ else }}
+		return 301 https://$host:{{ $external_https_port }}$request_uri;
 	{{ end }}
 	}
 }
diff --git a/test/pytest.sh b/test/pytest.sh
index b1514bf..28275e5 100755
--- a/test/pytest.sh
+++ b/test/pytest.sh
@@ -18,8 +18,8 @@ docker build -t nginx-proxy-tester -f "${DIR}/requirements/Dockerfile-nginx-prox
 
 # run the nginx-proxy-tester container setting the correct value for the working dir in order for 
 # docker-compose to work properly when run from within that container.
-exec docker run --rm \
-	-v ${DIR}:/${DIR} \
-	-w ${DIR} \
-	-v /var/run/docker.sock:/var/run/docker.sock \
-	nginx-proxy-tester ${ARGS}
+exec docker run --rm -it --name "nginx-proxy-pytest" \
+  --volume "/var/run/docker.sock:/var/run/docker.sock" \
+  --volume "${DIR}:${DIR}" \
+  --workdir "${DIR}" \
+  nginx-proxy-tester "${ARGS[@]}"
\ No newline at end of file
diff --git a/test/test_ssl/test_dhparam_generation.py b/test/test_ssl/test_dhparam_generation.py
deleted file mode 100644
index 1e5d154..0000000
--- a/test/test_ssl/test_dhparam_generation.py
+++ /dev/null
@@ -1,44 +0,0 @@
-import backoff
-import docker
-
-docker_client = docker.from_env()
-
-
-###############################################################################
-#
-# Tests helpers
-#
-###############################################################################
-
-@backoff.on_exception(backoff.constant, AssertionError, interval=2, max_tries=15, jitter=None)
-def assert_log_contains(expected_log_line):
-    """
-    Check that the nginx-proxy container log contains a given string.
-    The backoff decorator will retry the check 15 times with a 2 seconds delay.
-
-    :param expected_log_line: string to search for
-    :return: None
-    :raises: AssertError if the expected string is not found in the log
-    """
-    sut_container = docker_client.containers.get("nginxproxy")
-    docker_logs = sut_container.logs(stdout=True, stderr=True, stream=False, follow=False)
-    assert expected_log_line in docker_logs
-
-
-###############################################################################
-#
-# Tests
-#
-###############################################################################
-
-def test_dhparam_is_generated_if_missing(docker_compose):
-    sut_container = docker_client.containers.get("nginxproxy")
-    assert sut_container.status == "running"
-
-    assert_log_contains("A pre-generated dhparam.pem will be used for now")
-    assert_log_contains("dhparam generation complete, reloading nginx")
-
-    # Make sure the dhparam in use is not the default, pre-generated one
-    default_checksum = sut_container.exec_run("md5sum /app/dhparam.pem.default").split()
-    generated_checksum = sut_container.exec_run("md5sum /etc/nginx/dhparam/dhparam.pem").split()
-    assert default_checksum[0] != generated_checksum[0]
diff --git a/test/test_www_redirect.yml b/test/test_www_redirect.yml
index 3bb2831..66da08a 100644
--- a/test/test_www_redirect.yml
+++ b/test/test_www_redirect.yml
@@ -22,6 +22,5 @@ sut:
   image: nginxproxy/nginx-proxy:test
   volumes:
     - /var/run/docker.sock:/tmp/docker.sock:ro
-    - ./lib/ssl/dhparam.pem:/etc/nginx/dhparam/dhparam.pem:ro
     - ./test_ssl/certs:/etc/nginx/certs:ro
   
\ No newline at end of file