diff --git a/neon-0.31.2-lesstests.patch b/neon-0.31.2-lesstests.patch
new file mode 100644
index 0000000..1a88766
--- /dev/null
+++ b/neon-0.31.2-lesstests.patch
@@ -0,0 +1,14 @@
+
+The fail_nul_* tests are broken with OpenSSL configured to reject SHA-1 digests.
+
+--- neon-0.31.2/test/ssl.c.lesstests
++++ neon-0.31.2/test/ssl.c
+@@ -1932,7 +1932,7 @@
+     T(fail_ca_expired),
+ 
+     T(nulcn_identity),
+-#ifndef HAVE_GNUTLS
++#if 0
+     /* These certs were created with a SHA#1 digest so are rejected by GnuTLS. */
+     T(fail_nul_cn),
+     T(fail_nul_san),
diff --git a/neon.spec b/neon.spec
index 3025d6b..905a264 100644
--- a/neon.spec
+++ b/neon.spec
@@ -3,11 +3,12 @@
 Summary: An HTTP and WebDAV client library
 Name: neon
 Version: 0.31.2
-Release: 3%{?dist}
+Release: 4%{?dist}
 License: LGPLv2+
 URL: https://notroj.github.io/neon/
 Source0: https://notroj.github.io/neon/neon-%{version}.tar.gz
 Patch0: neon-0.27.0-multilib.patch
+Patch1: neon-0.31.2-lesstests.patch
 BuildRequires:  gcc-c++
 BuildRequires: expat-devel, openssl-devel, zlib-devel, krb5-devel, libproxy-devel
 BuildRequires: pkgconfig, pakchois-devel
@@ -37,6 +38,8 @@ The development library for the C language HTTP and WebDAV client library.
 %prep
 %setup -q
 %patch0 -p1 -b .multilib
+%patch1 -p1 -b .lesstests
+
 
 # prevent installation of HTML docs
 sed -ibak '/^install-docs/s/install-html//' Makefile.in
@@ -80,6 +83,9 @@ make %{?_smp_mflags} check
 %{_libdir}/*.so
 
 %changelog
+* Wed Aug 26 2020 Joe Orton <jorton@redhat.com> - 0.31.2-4
+- fix tests with current OpenSSL (#1863681)
+
 * Sat Aug 01 2020 Fedora Release Engineering <releng@fedoraproject.org> - 0.31.2-3
 - Second attempt - Rebuilt for
   https://fedoraproject.org/wiki/Fedora_33_Mass_Rebuild