diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index 5d9df9c1..40680fe3 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -11,10 +11,12 @@ jobs:
       fail-fast: false
       matrix:
         rust:
-          - 1.70.0
-          - stable
-          - beta
-          - nightly
+          # Don't pull in newest dependencies when using old Rust toolchain
+          - version: 1.70.0
+            env: SKIP_CARGO_UPDATE=1
+          - version: stable
+          - version: beta
+          - version: nightly
 
     steps:
       - uses: actions/checkout@v2
@@ -22,11 +24,11 @@ jobs:
       - uses: actions-rs/toolchain@v1
         with:
           profile: minimal
-          toolchain: ${{ matrix.rust }}
+          toolchain: ${{ matrix.rust.version }}
           override: true
 
       - name: test
-        run: ./capstone-rs/ci/test.sh
+        run: env ${{ matrix.rust.env }} ./capstone-rs/ci/test.sh
 
       - name: test (all features)
-        run: ALL_FEATURES=1 ./capstone-rs/ci/test.sh
+        run: env ${{ matrix.rust.env }} ALL_FEATURES=1 ./capstone-rs/ci/test.sh
diff --git a/capstone-rs/ci/test.sh b/capstone-rs/ci/test.sh
index 86af8015..3a665cc0 100755
--- a/capstone-rs/ci/test.sh
+++ b/capstone-rs/ci/test.sh
@@ -11,6 +11,7 @@
 # - JOB: {*test,valgrind-test,bench,cov}
 # - PROFILES: list of {debug,release} [debug release]
 # - SHOULD_FAIL: (disabled by default; set to non-empty string to enable)
+# - SKIP_CARGO_UPDATE: set to disable "cargo update" part of tests
 # - VALGRIND_TESTS: run tests under Valgrind
 
 set -euo pipefail
@@ -174,6 +175,7 @@ run_kcov() {
 
 cov() {
     echo "Running coverage"
+    cargo_update
 
     install_kcov
     cleanup_cov
@@ -193,6 +195,9 @@ cov() {
 }
 
 bench() {
+    echo "Running bench"
+    cargo_update
+
     ${CARGO} bench
 }
 
@@ -232,6 +237,8 @@ test_rust_file() {
 }
 
 run_tests() {
+    cargo_update
+
     TMPFILE="$(mktemp /tmp/capstone-rs.XXXXXXXXXX)"
     [ -f "$TMPFILE" ] || Error "Could not make temp file"
     for PROFILE in $PROFILES; do
@@ -284,6 +291,15 @@ run_tests() {
     rm "$TMPFILE"
 }
 
+cargo_update() {
+    if [ -z "${SKIP_CARGO_UPDATE:-}" ]; then
+        echo "Updating dependencies in Cargo.lock"
+        ${CARGO} update
+    else
+        echo "Skipping 'cargo update' since SKIP_CARGO_UPDATE is set"
+    fi
+}
+
 PROFILES="${PROFILES-debug}"
 for PROFILE in $PROFILES; do
     profile_args "$PROFILE"