diff --git a/.github/workflows/rust.yml b/.github/workflows/rust.yml
index db237a8..2214f4b 100644
--- a/.github/workflows/rust.yml
+++ b/.github/workflows/rust.yml
@@ -85,6 +85,35 @@ jobs:
         command: test
         args: --lib --no-default-features --features "alloc u32_backend"
 
+  nightly:
+    name: Test nightly compiler
+    runs-on: ubuntu-latest
+    steps:
+    - uses: actions/checkout@v2
+    - uses: actions-rs/toolchain@v1
+      with:
+        profile: minimal
+        toolchain: nightly
+        override: true
+    - uses: actions-rs/cargo@v1
+      with:
+        command: test
+        args: --features "nightly"
+
+  msrv:
+    name: Current MSRV is 1.41
+    runs-on: ubuntu-latest
+    steps:
+    - uses: actions/checkout@v2
+    - uses: actions-rs/toolchain@v1
+      with:
+        profile: minimal
+        toolchain: 1.41
+        override: true
+    - uses: actions-rs/cargo@v1
+      with:
+        command: build
+
   bench:
     name: Check that benchmarks compile
     runs-on: ubuntu-latest
diff --git a/Cargo.toml b/Cargo.toml
index 510f168..6dddb3b 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -50,7 +50,7 @@ serde = { version = "1.0", default-features = false, optional = true, features =
 # The original packed_simd package was orphaned, see
 # https://github.com/rust-lang/packed_simd/issues/303#issuecomment-701361161
 packed_simd = { version = "0.3.4", package = "packed_simd_2", features = ["into_bits"], optional = true }
-zeroize = { version = "1", default-features = false }
+zeroize = { version = "=1.3.0", default-features = false }
 fiat-crypto = { version = "0.1.6", optional = true}
 
 [features]