diff --git a/src/pushsource/_impl/backend/koji_source.py b/src/pushsource/_impl/backend/koji_source.py
index abe48ac1..6bdd282c 100644
--- a/src/pushsource/_impl/backend/koji_source.py
+++ b/src/pushsource/_impl/backend/koji_source.py
@@ -5,6 +5,7 @@
 
 from concurrent import futures
 from six.moves.queue import Queue, Empty
+import six
 from threading import Thread
 
 import koji
@@ -28,6 +29,10 @@
 LOG = logging.getLogger("pushsource")
 CACHE_LOCK = threading.RLock()
 
+# Arguments used for retry policy.
+# Provided so it can be overridden from tests to reduce time spent on retries.
+RETRY_ARGS = {}
+
 
 class ListArchivesCommand(object):
     def __init__(self, build):
@@ -205,7 +210,7 @@ def __init__(
         self._executor = (
             executor
             or Executors.thread_pool(name="pushsource-koji", max_workers=threads)
-            .with_retry()
+            .with_retry(**RETRY_ARGS)
             .with_cancel_on_shutdown()
         )
 
@@ -231,6 +236,28 @@ def _koji_session(self):
                 tls.koji_session = koji.ClientSession(self._url)
         return tls.koji_session
 
+    def _koji_check(self):
+        # Do a basic connection check with koji.
+        # If this succeeds, we can be reasonably sure that the koji connection is
+        # more or less working.
+        try:
+            version = self._executor.submit(self._koji_get_version).result()
+        except Exception as ex:  # pylint: disable=broad-except
+            # TODO: drop this log when py2 support is dropped.
+            # It's only here because py2 has no exception chaining.
+            msg = "Communication error with koji at %s" % self._url
+            LOG.exception(msg)
+
+            six.raise_from(RuntimeError(msg), ex)
+
+        LOG.debug("Connected to koji %s at %s", version, self._url)
+
+    def _koji_get_version(self):
+        with CACHE_LOCK:
+            if "koji_version" not in self._cache:
+                self._cache["koji_version"] = self._koji_session.getVersion()
+            return self._cache["koji_version"]
+
     def _get_rpm(self, rpm):
         return self._cache["rpm"][rpm]
 
@@ -573,6 +600,22 @@ def _do_fetch(self, koji_queue, exceptions):
             raise
 
     def __iter__(self):
+        # Try a (blocking) call to koji before anything else.
+        #
+        # The reasons for this are:
+        #
+        # - give an error which is hopefully easier to understand if the
+        #   koji connection is completely broken (e.g. caller provides bogus
+        #   URL)
+        #
+        # - work around pyasn1 bug https://github.com/etingof/pyasn1/issues/53
+        #   which affects some (ancient) environments. That thread-safety bug
+        #   can cause parsing of subjectAltName to fail if it first occurs from
+        #   multiple threads simultaneously. Doing a warm-up from one thread
+        #   before we spawn multiple threads is a way to avoid this.
+        #
+        self._koji_check()
+
         # Queue holding all requests we need to make to koji.
         # We try to fetch as much as we can early to make efficient use
         # of multicall.
diff --git a/tests/koji/conftest.py b/tests/koji/conftest.py
index eb8b54d7..9d67af3d 100644
--- a/tests/koji/conftest.py
+++ b/tests/koji/conftest.py
@@ -1,6 +1,8 @@
 from pytest import fixture
 from mock import patch
 
+from pushsource._impl.backend import koji_source
+
 from .fake_koji import FakeKojiController
 
 
@@ -15,3 +17,10 @@ def fake_koji():
 @fixture
 def koji_dir(tmpdir):
     yield str(tmpdir.mkdir("koji"))
+
+
+@fixture(autouse=True)
+def fast_retry(monkeypatch):
+    # Force a custom retry policy so that tests which simulate errors
+    # don't spent as much time retrying as they would in production.
+    monkeypatch.setattr(koji_source, "RETRY_ARGS", {"max_sleep": 0.0001})
diff --git a/tests/koji/fake_koji.py b/tests/koji/fake_koji.py
index 3e914d55..df72893e 100644
--- a/tests/koji/fake_koji.py
+++ b/tests/koji/fake_koji.py
@@ -158,6 +158,9 @@ def _return_or_raise(self, value):
             raise value
         return value
 
+    def getVersion(self):
+        return "fake-version"
+
     def getRPM(self, rpm):
         return self._return_or_raise(self._ctrl.rpm_data.get(rpm))
 
diff --git a/tests/koji/test_koji.py b/tests/koji/test_koji.py
index c5ccad57..68fa415d 100644
--- a/tests/koji/test_koji.py
+++ b/tests/koji/test_koji.py
@@ -18,13 +18,27 @@ def test_get_koji():
     assert Source.get("koji:https://koji.example.com/")
 
 
-def test_koji_empty():
+def test_koji_empty(fake_koji):
     """Empty koji source yields no push items"""
 
     source = Source.get("koji:https://koji.example.com/")
     assert list(source) == []
 
 
+def test_koji_connect_error():
+    """Source raises a reasonable error if server can't be contacted"""
+
+    # Note: fake_koji fixture not used here, so this will really try to connect
+    source = Source.get("koji:https://localhost:1234/this-aint-koji")
+    with raises(RuntimeError) as exc_info:
+        list(source)
+
+    assert (
+        "Communication error with koji at https://localhost:1234/this-aint-koji"
+        in str(exc_info.value)
+    )
+
+
 def test_koji_nobuild(fake_koji):
     """koji source referencing nonexistent build will fail"""