diff --git a/tests/ChangeLog b/tests/ChangeLog
index 4b79696c..36bc35dc 100644
--- a/tests/ChangeLog
+++ b/tests/ChangeLog
@@ -2,7 +2,8 @@
 
 	* Test-proxied-https-auth.px: Shift exit code so it falls in the
 	lower bits, and actually fails when it should. Use dynamic port,
-	instead of static port.
+	instead of static port. Only run the test if our Wget was built
+	with HTTPS support.
 
 	* certs/server-cert.pem, certs/server-key.pem: Apparently failed
 	to add these from 1.11.x repo. Fixed.
diff --git a/tests/Test-proxied-https-auth.px b/tests/Test-proxied-https-auth.px
index 182c9dbf..a2efe5eb 100755
--- a/tests/Test-proxied-https-auth.px
+++ b/tests/Test-proxied-https-auth.px
@@ -3,6 +3,16 @@ use warnings;
 use strict;
 
 use WgetTest;  # For $WGETPATH.
+
+# Have we even built an HTTPS-supporting Wget?
+{
+    my @version_lines = `${WgetTest::WGETPATH} --version`;
+    unless (grep /\+(openssl|gnutls)/, @version_lines) {
+        print "Not running test: Wget under test doesn't support HTTPS.\n";
+        exit 0;
+    }
+}
+
 use HTTP::Daemon;
 use HTTP::Request;
 use IO::Socket::SSL;