diff --git a/.cirrus.yml b/.cirrus.yml
index 585dd24f6a..f3b18d6a35 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -12,7 +12,7 @@ task:
     image: freebsd-11-4-release-amd64
   setup_script:
     - fetch https://sh.rustup.rs -o rustup.sh
-    - sh rustup.sh -y --profile=minimal --default-toolchain 1.36.0
+    - sh rustup.sh -y --profile=minimal --default-toolchain 1.40.0
     - $HOME/.cargo/bin/rustup target add i686-unknown-freebsd
   amd64_test_script:
     - . $HOME/.cargo/env
@@ -42,7 +42,7 @@ task:
     image: catalina-xcode
   setup_script:
     - curl --proto '=https' --tlsv1.2 -sSf -o rustup.sh https://sh.rustup.rs
-    - sh rustup.sh -y --profile=minimal --default-toolchain 1.36.0
+    - sh rustup.sh -y --profile=minimal --default-toolchain 1.40.0
     - . $HOME/.cargo/env
     - bash ci/install.sh
   script:
@@ -92,7 +92,7 @@ docker_builder:
   setup_script:
     - mkdir /tmp/home
     - curl --proto '=https' --tlsv1.2 -sSf -o rustup.sh https://sh.rustup.rs
-    - sh rustup.sh -y --profile=minimal --default-toolchain 1.36.0
+    - sh rustup.sh -y --profile=minimal --default-toolchain 1.40.0
     - . $HOME/.cargo/env
     - bash ci/install.sh
   script:
@@ -110,11 +110,11 @@ task:
     - name: Linux x86_64
       env:
         TARGET: x86_64-unknown-linux-gnu
-        TOOLCHAIN: 1.36.0
+        TOOLCHAIN: 1.40.0
     - name: Linux x86_64 musl
       env:
         TARGET: x86_64-unknown-linux-musl
-        TOOLCHAIN: 1.36.0
+        TOOLCHAIN: 1.40.0
   container:
     image: rust:1.36
   setup_script:
diff --git a/CHANGELOG.md b/CHANGELOG.md
index a110f6500b..2201504d1b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,9 @@ This project adheres to [Semantic Versioning](http://semver.org/).
 ### Fixed
 ### Changed
 
+- Minimum supported Rust version is now 1.40.0.
+  ([#1356](https://github.com/nix-rust/nix/pull/1356))
+
 - i686-apple-darwin has been demoted to Tier 2 support, because it's deprecated
   by Xcode.
   (#[1350](https://github.com/nix-rust/nix/pull/1350))
diff --git a/README.md b/README.md
index d6c341280c..36df3e3990 100644
--- a/README.md
+++ b/README.md
@@ -85,7 +85,7 @@ Tier 3:
 
 ## Usage
 
-`nix` requires Rust 1.36.0 or newer.
+`nix` requires Rust 1.40.0 or newer.
 
 To use `nix`, add this to your `Cargo.toml`:
 
diff --git a/test/sys/test_aio.rs b/test/sys/test_aio.rs
index 37ad32578d..3878da94a6 100644
--- a/test/sys/test_aio.rs
+++ b/test/sys/test_aio.rs
@@ -137,6 +137,9 @@ fn test_fsync_error() {
 // in Travis's version of glibc or Linux.  Either way, we must skip the test.
 // https://github.com/nix-rust/nix/issues/1099
 #[cfg_attr(target_os = "linux", ignore)]
+// On Cirrus, aio_suspend is failing with EINVAL
+// https://github.com/nix-rust/nix/issues/1361
+#[cfg_attr(target_os = "macos", ignore)]
 fn test_aio_suspend() {
     const INITIAL: &[u8] = b"abcdef123456";
     const WBUF: &[u8] = b"CDEFG";
diff --git a/test/test_unistd.rs b/test/test_unistd.rs
index a5c6a33278..d169d6e099 100644
--- a/test/test_unistd.rs
+++ b/test/test_unistd.rs
@@ -1064,13 +1064,7 @@ fn test_ttyname_not_pty() {
 }
 
 #[test]
-#[cfg(all(not(target_os = "redox"), not(target_env = "musl")))]
+#[cfg(all(not(target_os = "redox")))]
 fn test_ttyname_invalid_fd() {
     assert_eq!(ttyname(-1), Err(Error::Sys(Errno::EBADF)));
 }
-
-#[test]
-#[cfg(all(not(target_os = "redox"), target_env = "musl"))]
-fn test_ttyname_invalid_fd() {
-    assert_eq!(ttyname(-1), Err(Error::Sys(Errno::ENOTTY)));
-}