diff --git a/parsl/executors/high_throughput/interchange.py b/parsl/executors/high_throughput/interchange.py
index 12d3e07f31..61fa29f0f7 100644
--- a/parsl/executors/high_throughput/interchange.py
+++ b/parsl/executors/high_throughput/interchange.py
@@ -5,13 +5,13 @@
 import os
 import pickle
 import platform
-import queue
 import sys
 import threading
 import time
 from typing import Any, Dict, List, NoReturn, Optional, Sequence, Set, Tuple, cast
 
 import zmq
+from sortedcontainers import SortedList
 
 from parsl import curvezmq
 from parsl.addresses import tcp_url
@@ -131,7 +131,7 @@ def __init__(self,
         self.hub_address = hub_address
         self.hub_zmq_port = hub_zmq_port
 
-        self.pending_task_queue: queue.Queue[Any] = queue.Queue(maxsize=10 ** 6)
+        self.pending_task_queue: SortedList[Any] = SortedList(key=lambda msg: -msg['resource_spec']['priority'])
         self.count = 0
 
         self.worker_ports = worker_ports
@@ -192,12 +192,9 @@ def get_tasks(self, count: int) -> Sequence[dict]:
         """
         tasks = []
         for _ in range(0, count):
-            try:
-                x = self.pending_task_queue.get(block=False)
-            except queue.Empty:
-                break
-            else:
-                tasks.append(x)
+            if len(self.pending_task_queue) > 0:
+                x = self.pending_task_queue.pop(-1)
+            tasks.append(x)
 
         return tasks
 
@@ -215,11 +212,14 @@ def task_puller(self) -> NoReturn:
                 msg = self.task_incoming.recv_pyobj()
             except zmq.Again:
                 # We just timed out while attempting to receive
-                logger.debug("zmq.Again with {} tasks in internal queue".format(self.pending_task_queue.qsize()))
+                logger.debug("zmq.Again with {} tasks in internal queue".format(len(self.pending_task_queue)))
                 continue
 
+            resource_spec = msg.get('resource_spec', {})
+            resource_spec.setdefault("priority", float('inf'))
+            msg['resource_spec'] = resource_spec
             logger.debug("putting message onto pending_task_queue")
-            self.pending_task_queue.put(msg)
+            self.pending_task_queue.add(msg)
             task_counter += 1
             logger.debug(f"Fetched {task_counter} tasks so far")
 
@@ -476,10 +476,10 @@ def process_tasks_to_send(self, interesting_managers: Set[bytes]) -> None:
             len(self._ready_managers)
         )
 
-        if interesting_managers and not self.pending_task_queue.empty():
+        if interesting_managers and (len(self.pending_task_queue) != 0):
             shuffled_managers = self.manager_selector.sort_managers(self._ready_managers, interesting_managers)
 
-            while shuffled_managers and not self.pending_task_queue.empty():  # cf. the if statement above...
+            while shuffled_managers and (len(self.pending_task_queue) != 0):  # cf. the if statement above...
                 manager_id = shuffled_managers.pop()
                 m = self._ready_managers[manager_id]
                 tasks_inflight = len(m['tasks'])
diff --git a/parsl/tests/test_htex/test_priority_queue.py b/parsl/tests/test_htex/test_priority_queue.py
new file mode 100644
index 0000000000..f36a64ae4b
--- /dev/null
+++ b/parsl/tests/test_htex/test_priority_queue.py
@@ -0,0 +1,53 @@
+import pytest
+
+import parsl
+from parsl.app.app import bash_app, python_app
+from parsl.config import Config
+from parsl.executors import HighThroughputExecutor
+from parsl.executors.high_throughput.manager_selector import (
+    ManagerSelector,
+    RandomManagerSelector,
+)
+from parsl.launchers import WrappedLauncher
+from parsl.providers import LocalProvider
+from parsl.usage_tracking.levels import LEVEL_1
+
+
+@parsl.python_app
+def fake_task(parsl_resource_specification={'priority': 1}):
+    import time
+    return time.time()
+
+
+@pytest.mark.local
+def test_priority_queue():
+    p = LocalProvider(
+        init_blocks=0,
+        max_blocks=0,
+        min_blocks=0,
+    )
+
+    htex = HighThroughputExecutor(
+        label="htex_local",
+        max_workers_per_node=1,
+        manager_selector=RandomManagerSelector(),
+        provider=p,
+    )
+
+    config = Config(
+        executors=[htex],
+        strategy="htex_auto_scale",
+        usage_tracking=LEVEL_1,
+    )
+
+    with parsl.load(config):
+        futures = {}
+        for priority in range(10, 0, -1):
+            spec = {'priority': priority}
+            futures[priority] = fake_task(parsl_resource_specification=spec)
+
+        p.max_blocks = 1
+        results = {priority: future.result() for priority, future in futures.items()}
+        sorted_results = dict(sorted(results.items(), key=lambda item: item[1]))
+        sorted_priorities = list(sorted_results.keys())
+        assert sorted_priorities == sorted(sorted_priorities)
diff --git a/test-requirements.txt b/test-requirements.txt
index 82ec5172c2..e043171e8f 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -16,6 +16,7 @@ mpi4py
 # (where it's specified in setup.py)
 sqlalchemy>=1.4,<2
 sqlalchemy2-stubs
+sortedcontainers-stubs
 
 Sphinx==4.5.0
 twine