diff --git a/.travis.yml b/.travis.yml
index 2832a9cac4..e693535746 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -59,6 +59,8 @@ jobs:
         - *common_packages
         - krb5-user
         - libssh2-1-dev
+        - libbrotli-dev
+        - libzstd-dev
   - env:
     - T=normal C=--with-libssh
     # Avoid bionic, its pre-release libssh version triggers deprecation warnings.
diff --git a/tests/valgrind.supp b/tests/valgrind.supp
index 10b07314a9..6d72a8bb40 100644
--- a/tests/valgrind.supp
+++ b/tests/valgrind.supp
@@ -1,3 +1,35 @@
+{
+   zstd_decompression-1.3.3-on-Ubuntu-18.04
+   Memcheck:Cond
+   fun:ZSTD_decompressStream
+   fun:zstd_unencode_write
+   fun:Curl_unencode_write
+   fun:readwrite_data
+   fun:Curl_readwrite
+   fun:multi_runsingle
+   fun:curl_multi_perform
+   fun:easy_transfer
+   fun:easy_perform
+   fun:curl_easy_perform
+   fun:serial_transfers
+   fun:run_all_transfers
+   fun:operate
+   fun:main
+}
+
+{
+   zstd_decompression-1.3.3-on-Ubuntu-18.04-nondebug
+   Memcheck:Cond
+   fun:ZSTD_decompressStream
+   fun:zstd_unencode_write
+   fun:Curl_readwrite
+   fun:multi_runsingle
+   fun:curl_multi_perform
+   fun:curl_easy_perform
+   fun:operate
+   fun:main
+}
+
 {
    libidn-idna_to_ascii-error
    Memcheck:Addr4