diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 786c59ab..38c646f4 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -162,6 +162,29 @@ jobs:
     - name: Run tests without any features enabled (core-only)
       run: cargo test --verbose --no-default-features
 
+  # This job uses a target to build the memchr crate on x86-64 but *without*
+  # SSE/AVX target features. This is relevant for virtually all OS kernels.
+  build-for-x86-64-but-non-sse-target:
+    runs-on: ubuntu-latest
+    steps:
+    - name: Checkout repository
+      uses: actions/checkout@v3
+    - name: Install Rust
+      uses: dtolnay/rust-toolchain@master
+      with:
+        toolchain: stable
+        targets: x86_64-unknown-none
+    - name: Build for x86_64-unknown-none with only 'alloc' enabled
+      run: cargo build --verbose --no-default-features --features alloc --target x86_64-unknown-none
+    - name: Run tests for x86_64-unknown-linux-gnu without SSE
+      run: cargo test --verbose
+      env:
+        RUSTFLAGS: -C target-feature=-mmx,-sse,-sse2,-sse3,-ssse3,-sse4.1,-sse4.2,-3dnow,-3dnowa,-avx,-avx2,+soft-float
+    - name: Run tests for x86_64-unknown-linux-gnu without SSE with only 'alloc' enabled
+      run: cargo test --verbose --no-default-features --features alloc
+      env:
+        RUSTFLAGS: -C target-feature=-mmx,-sse,-sse2,-sse3,-ssse3,-sse4.1,-sse4.2,-3dnow,-3dnowa,-avx,-avx2,+soft-float
+
   # This job runs a stripped down version of CI to test the MSRV. The specific
   # reason for doing this is that dev-dependencies tend to evolve more quickly.
   # There isn't as tight of a control on them because, well, they're only used
diff --git a/src/tests/x86_64-soft_float.json b/src/tests/x86_64-soft_float.json
deleted file mode 100644
index b77649ef..00000000
--- a/src/tests/x86_64-soft_float.json
+++ /dev/null
@@ -1,15 +0,0 @@
-{
-    "llvm-target": "x86_64-unknown-none",
-    "target-endian": "little",
-    "target-pointer-width": "64",
-    "target-c-int-width": "32",
-    "os": "none",
-    "arch": "x86_64",
-    "data-layout": "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-f80:128-n8:16:32:64-S128",
-    "linker-flavor": "ld.lld",
-    "linker": "rust-lld",
-    "features": "-mmx,-sse,-sse2,-sse3,-ssse3,-sse4.1,-sse4.2,-3dnow,-3dnowa,-avx,-avx2,+soft-float",
-    "executables": true,
-    "disable-redzone": true,
-    "panic-strategy": "abort"
-}