diff --git a/.dockerignore b/.dockerignore
new file mode 100644
index 0000000..54f1d00
--- /dev/null
+++ b/.dockerignore
@@ -0,0 +1 @@
+/releases
diff --git a/.github/workflows/linux-ci.yml b/.github/workflows/linux-ci.yml
index 0d45df3..c20c452 100644
--- a/.github/workflows/linux-ci.yml
+++ b/.github/workflows/linux-ci.yml
@@ -15,7 +15,7 @@ jobs:
       - name: Set up Go
         uses: actions/setup-go@v3
         with:
-          go-version-file: 'go.mod'
+          go-version-file: "go.mod"
 
       # golangci-lint is required by test.sh. Latest version here if you want
       # to bump it, version number is at the end of the "curl | sh"
@@ -25,3 +25,4 @@ jobs:
         run: curl -sSfL https://raw.githubusercontent.com/golangci/golangci-lint/master/install.sh | sh -s -- -b "$(go env GOPATH)"/bin v1.51.2
 
       - run: ./test.sh
+      - run: GOARCH=386 ./test.sh
diff --git a/Dockerfile-test-386 b/Dockerfile-test-386
new file mode 100644
index 0000000..e7acd19
--- /dev/null
+++ b/Dockerfile-test-386
@@ -0,0 +1,13 @@
+# Run the tests in 32 bit mode:
+# docker build . -f Dockerfile-test-386
+
+FROM golang:1.20
+
+WORKDIR /moar
+
+COPY go.mod go.sum ./
+RUN go mod download
+
+COPY . .
+
+RUN GOARCH=386 go test -v ./...
diff --git a/README.md b/README.md
index 6c27004..aca6749 100644
--- a/README.md
+++ b/README.md
@@ -184,6 +184,9 @@ Run tests:
 ./test.sh
 ```
 
+To run tests in 32 bit mode, either do `GOARCH=386 ./test.sh` if you're on
+Linux, or `docker build . -f Dockerfile-test-386` (tested on macOS).
+
 Run microbenchmarks:
 
 ```bash