diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index 40f5d3579..6de03d4d4 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -10,6 +10,7 @@ jobs:
     name: Test
     runs-on: ${{ matrix.os }}
     strategy:
+      fail-fast: false
       matrix:
         build: [x86_64, i686, x86_64-musl, mingw, system-curl, openssl-110, x86_64-beta, x86_64-nightly, macos, win64, win32]
         include:
diff --git a/ci/Dockerfile-musl b/ci/Dockerfile-musl
index fcb9433fc..ef52a9280 100644
--- a/ci/Dockerfile-musl
+++ b/ci/Dockerfile-musl
@@ -3,16 +3,4 @@ FROM ubuntu:16.04
 RUN apt-get update
 RUN apt-get install -y --no-install-recommends \
   gcc ca-certificates make libc6-dev curl \
-  musl-tools
-
-RUN \
-  curl -L https://www.openssl.org/source/old/1.0.2/openssl-1.0.2g.tar.gz | tar xzf - && \
-  cd openssl-1.0.2g && \
-  CC=musl-gcc ./Configure --prefix=/openssl no-dso linux-x86_64 -fPIC && \
-  make -j10 && \
-  make install && \
-  cd .. && \
-  rm -rf openssl-1.0.2g
-
-ENV OPENSSL_STATIC=1 \
-    OPENSSL_DIR=/openssl
+  musl-tools perl
diff --git a/ci/run.sh b/ci/run.sh
index 5276c2d9d..82b547f94 100755
--- a/ci/run.sh
+++ b/ci/run.sh
@@ -2,9 +2,14 @@
 
 set -ex
 
-cargo test --target $TARGET --no-run
+# For musl on CI always use openssl-src dependency and build from there.
+if [ "$TARGET" = "x86_64-unknown-linux-musl" ]; then
+  features="--features static-ssl"
+fi
+
+cargo test --target $TARGET --no-run $features
 # First test with no extra protocols enabled.
-cargo test --target $TARGET --no-run --features static-curl
+cargo test --target $TARGET --no-run --features static-curl $features
 # Then with rustls TLS backend.
 #
 # Note: Cross-compiling rustls on windows doesn't work due to requiring some
@@ -16,22 +21,22 @@ cargo test --target $TARGET --no-run --features static-curl
 # inconvenience for me.
 if [ "$TARGET" != "x86_64-pc-windows-gnu" ] && [ "$TARGET" != "i686-pc-windows-msvc" ]
 then
-    cargo test --target $TARGET --no-run --features rustls,static-curl
+    cargo test --target $TARGET --no-run --features rustls,static-curl $features
 fi
 # Then with all extra protocols enabled.
-cargo test --target $TARGET --no-run --features static-curl,protocol-ftp,ntlm
+cargo test --target $TARGET --no-run --features static-curl,protocol-ftp,ntlm $features
 if [ -z "$NO_RUN" ]; then
-    cargo test --target $TARGET
-    cargo test --target $TARGET --features static-curl
-    cargo test --target $TARGET --features static-curl,protocol-ftp
+    cargo test --target $TARGET $features
+    cargo test --target $TARGET --features static-curl $features
+    cargo test --target $TARGET --features static-curl,protocol-ftp $features
 
     # Note that `-Clink-dead-code` is passed here to suppress `--gc-sections` to
     # help confirm that we're compiling everything necessary for curl itself.
     RUSTFLAGS=-Clink-dead-code \
-    cargo run --manifest-path systest/Cargo.toml --target $TARGET
+    cargo run --manifest-path systest/Cargo.toml --target $TARGET $features
     RUSTFLAGS=-Clink-dead-code \
-    cargo run --manifest-path systest/Cargo.toml --target $TARGET --features curl-sys/static-curl,curl-sys/protocol-ftp
+    cargo run --manifest-path systest/Cargo.toml --target $TARGET --features curl-sys/static-curl,curl-sys/protocol-ftp $features
 
-    cargo doc --no-deps --target $TARGET
-    cargo doc --no-deps -p curl-sys --target $TARGET
+    cargo doc --no-deps --target $TARGET $features
+    cargo doc --no-deps -p curl-sys --target $TARGET $features
 fi
diff --git a/systest/Cargo.toml b/systest/Cargo.toml
index 3a28375fe..aa268ade1 100644
--- a/systest/Cargo.toml
+++ b/systest/Cargo.toml
@@ -13,3 +13,6 @@ libc = "0.2"
 [build-dependencies]
 ctest2 = "0.4"
 cc = "1.0"
+
+[features]
+static-ssl = ['curl-sys/static-ssl']