diff --git a/.cirrus.yml b/.cirrus.yml
index 63a1de956..1cd106778 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -1,4 +1,4 @@
-only_if: $CIRRUS_TAG == '' && ($CIRRUS_PR != '' || $CIRRUS_BRANCH == 'master' || $CIRRUS_BRANCH == 'staging')
+only_if: $CIRRUS_TAG == '' && ($CIRRUS_PR != '' || $CIRRUS_BRANCH == 'staging')
 auto_cancellation: $CIRRUS_BRANCH != 'master'
 env:
   CARGO_INCREMENTAL: '0'
diff --git a/ci/no_atomic.sh b/ci/no_atomic.sh
index 186b8bcce..10bbf61dd 100755
--- a/ci/no_atomic.sh
+++ b/ci/no_atomic.sh
@@ -11,6 +11,7 @@ cd "$(dirname "$0")"/..
 file="no_atomic.rs"
 
 no_atomic_cas=()
+no_atomic_32=()
 no_atomic_64=()
 no_atomic=()
 for target in $(rustc --print target-list); do
@@ -27,13 +28,11 @@ for target in $(rustc --print target-list); do
         # `"target-pointer-width" == "32"`, so assuming them `"max-atomic-width" == 32`
         # for now.
         32 | null) no_atomic_64+=("${target}") ;;
+        16) no_atomic_32+=("${target}") ;;
         # `"max-atomic-width" == 0` means that atomic is not supported at all.
-        0)
-            no_atomic_64+=("${target}")
-            no_atomic+=("${target}")
-            ;;
+        0) no_atomic+=("${target}") ;;
         64 | 128) ;;
-        # There is no `"max-atomic-width" == 16` or `"max-atomic-width" == 8` targets.
+        # There is no `"max-atomic-width" == 8` targets.
         *) exit 1 ;;
     esac
     case "${min_atomic_width}" in
@@ -63,6 +62,15 @@ done
 cat >>"${file}" <<EOF
 ];
 
+#[allow(dead_code)] // Only crossbeam-utils uses this.
+const NO_ATOMIC_32: &[&str] = &[
+EOF
+for target in "${no_atomic_32[@]}"; do
+    echo "    \"${target}\"," >>"${file}"
+done
+cat >>"${file}" <<EOF
+];
+
 #[allow(dead_code)] // Only crossbeam-utils uses this.
 const NO_ATOMIC: &[&str] = &[
 EOF
diff --git a/crossbeam-utils/build.rs b/crossbeam-utils/build.rs
index 39785f030..120bbcff5 100644
--- a/crossbeam-utils/build.rs
+++ b/crossbeam-utils/build.rs
@@ -52,6 +52,10 @@ fn main() {
     }
     if NO_ATOMIC.contains(&&*target) {
         println!("cargo:rustc-cfg=crossbeam_no_atomic");
+        println!("cargo:rustc-cfg=crossbeam_no_atomic_32");
+        println!("cargo:rustc-cfg=crossbeam_no_atomic_64");
+    } else if NO_ATOMIC_32.contains(&&*target) {
+        println!("cargo:rustc-cfg=crossbeam_no_atomic_32");
         println!("cargo:rustc-cfg=crossbeam_no_atomic_64");
     } else if NO_ATOMIC_64.contains(&&*target) {
         println!("cargo:rustc-cfg=crossbeam_no_atomic_64");
diff --git a/crossbeam-utils/src/atomic/atomic_cell.rs b/crossbeam-utils/src/atomic/atomic_cell.rs
index c60efbc94..289993395 100644
--- a/crossbeam-utils/src/atomic/atomic_cell.rs
+++ b/crossbeam-utils/src/atomic/atomic_cell.rs
@@ -695,8 +695,14 @@ impl_arithmetic!(u8, atomic::AtomicU8, "let a = AtomicCell::new(7u8);");
 impl_arithmetic!(i8, atomic::AtomicI8, "let a = AtomicCell::new(7i8);");
 impl_arithmetic!(u16, atomic::AtomicU16, "let a = AtomicCell::new(7u16);");
 impl_arithmetic!(i16, atomic::AtomicI16, "let a = AtomicCell::new(7i16);");
+#[cfg(not(crossbeam_no_atomic_32))]
 impl_arithmetic!(u32, atomic::AtomicU32, "let a = AtomicCell::new(7u32);");
+#[cfg(not(crossbeam_no_atomic_32))]
 impl_arithmetic!(i32, atomic::AtomicI32, "let a = AtomicCell::new(7i32);");
+#[cfg(crossbeam_no_atomic_32)]
+impl_arithmetic!(u32, fallback, "let a = AtomicCell::new(7u32);");
+#[cfg(crossbeam_no_atomic_32)]
+impl_arithmetic!(i32, fallback, "let a = AtomicCell::new(7i32);");
 #[cfg(not(crossbeam_no_atomic_64))]
 impl_arithmetic!(u64, atomic::AtomicU64, "let a = AtomicCell::new(7u64);");
 #[cfg(not(crossbeam_no_atomic_64))]
diff --git a/crossbeam-utils/src/atomic/consume.rs b/crossbeam-utils/src/atomic/consume.rs
index 80a88829b..d40dd72dc 100644
--- a/crossbeam-utils/src/atomic/consume.rs
+++ b/crossbeam-utils/src/atomic/consume.rs
@@ -83,7 +83,9 @@ impl_atomic!(AtomicU8, u8);
 impl_atomic!(AtomicI8, i8);
 impl_atomic!(AtomicU16, u16);
 impl_atomic!(AtomicI16, i16);
+#[cfg(not(crossbeam_no_atomic_32))]
 impl_atomic!(AtomicU32, u32);
+#[cfg(not(crossbeam_no_atomic_32))]
 impl_atomic!(AtomicI32, i32);
 #[cfg(not(crossbeam_no_atomic_64))]
 impl_atomic!(AtomicU64, u64);
diff --git a/crossbeam-utils/src/lib.rs b/crossbeam-utils/src/lib.rs
index 191c5a17d..6a2671710 100644
--- a/crossbeam-utils/src/lib.rs
+++ b/crossbeam-utils/src/lib.rs
@@ -72,9 +72,10 @@ mod primitive {
             pub(crate) use core::sync::atomic::spin_loop_hint;
             #[cfg(not(crossbeam_no_atomic))]
             pub(crate) use core::sync::atomic::{
-                AtomicBool, AtomicI16, AtomicI32, AtomicI8, AtomicIsize, AtomicU16, AtomicU32,
-                AtomicU8, AtomicUsize,
+                AtomicBool, AtomicI16, AtomicI8, AtomicIsize, AtomicU16, AtomicU8, AtomicUsize,
             };
+            #[cfg(not(crossbeam_no_atomic_32))]
+            pub(crate) use core::sync::atomic::{AtomicI32, AtomicU32};
             #[cfg(not(crossbeam_no_atomic_64))]
             pub(crate) use core::sync::atomic::{AtomicI64, AtomicU64};
         }
diff --git a/no_atomic.rs b/no_atomic.rs
index a268fe6c8..a3a217099 100644
--- a/no_atomic.rs
+++ b/no_atomic.rs
@@ -26,21 +26,18 @@ const NO_ATOMIC_64: &[&str] = &[
     "armv5te-unknown-linux-musleabi",
     "armv5te-unknown-linux-uclibceabi",
     "armv6k-nintendo-3ds",
-    "avr-unknown-gnu-atmega328",
     "hexagon-unknown-linux-musl",
     "m68k-unknown-linux-gnu",
     "mips-unknown-linux-gnu",
     "mips-unknown-linux-musl",
     "mips-unknown-linux-uclibc",
     "mipsel-sony-psp",
-    "mipsel-sony-psx",
     "mipsel-unknown-linux-gnu",
     "mipsel-unknown-linux-musl",
     "mipsel-unknown-linux-uclibc",
     "mipsel-unknown-none",
     "mipsisa32r6-unknown-linux-gnu",
     "mipsisa32r6el-unknown-linux-gnu",
-    "msp430-none-elf",
     "powerpc-unknown-freebsd",
     "powerpc-unknown-linux-gnu",
     "powerpc-unknown-linux-gnuspe",
@@ -51,11 +48,9 @@ const NO_ATOMIC_64: &[&str] = &[
     "powerpc-wrs-vxworks-spe",
     "riscv32gc-unknown-linux-gnu",
     "riscv32gc-unknown-linux-musl",
-    "riscv32i-unknown-none-elf",
-    "riscv32im-unknown-none-elf",
     "riscv32imac-unknown-none-elf",
     "riscv32imac-unknown-xous-elf",
-    "riscv32imc-unknown-none-elf",
+    "sparc-unknown-linux-gnu",
     "sparc-unknown-none-elf",
     "thumbv4t-none-eabi",
     "thumbv5te-none-eabi",
@@ -69,8 +64,12 @@ const NO_ATOMIC_64: &[&str] = &[
 ];
 
 #[allow(dead_code)] // Only crossbeam-utils uses this.
-const NO_ATOMIC: &[&str] = &[
+const NO_ATOMIC_32: &[&str] = &[
     "avr-unknown-gnu-atmega328",
+];
+
+#[allow(dead_code)] // Only crossbeam-utils uses this.
+const NO_ATOMIC: &[&str] = &[
     "bpfeb-unknown-none",
     "bpfel-unknown-none",
     "mipsel-sony-psx",