diff --git a/changes/bug20588 b/changes/bug20588
new file mode 100644
index 000000000..be199b2de
--- /dev/null
+++ b/changes/bug20588
@@ -0,0 +1,3 @@
+  o Minor bugfixes (portability):
+    - Fix compilation with OpenSSL 1.1 and less commonly-used
+      CPU architectures. Closes ticket 20588.
diff --git a/src/common/aes.c b/src/common/aes.c
index ef94d8a75..35c2d1e3a 100644
--- a/src/common/aes.c
+++ b/src/common/aes.c
@@ -56,7 +56,14 @@ ENABLE_GCC_WARNING(redundant-decls)
  * gives us, and the best possible counter-mode implementation, and combine
  * them.
  */
-#if OPENSSL_VERSION_NUMBER >= OPENSSL_V_NOPATCH(1,0,1) &&               \
+#if OPENSSL_VERSION_NUMBER >= OPENSSL_V_NOPATCH(1,1,0)
+
+/* With newer OpenSSL versions, the older fallback modes don't compile.  So
+ * don't use them, even if we lack specific acceleration. */
+
+#define USE_EVP_AES_CTR
+
+#elif OPENSSL_VERSION_NUMBER >= OPENSSL_V_NOPATCH(1,0,1) &&               \
   (defined(__i386) || defined(__i386__) || defined(_M_IX86) ||          \
    defined(__x86_64) || defined(__x86_64__) ||                          \
    defined(_M_AMD64) || defined(_M_X64) || defined(__INTEL__))          \