diff --git a/.gitignore b/.gitignore
index 7e85a917bd..bd5163ee7a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -8,7 +8,7 @@ __pycache__
 build
 dist
 *.egg-info
-pkg/dockerfile/embed/*.whl
+pkg/dockerfile/embed/*
 # Used by a vim plugin (projectionist)
 .projections.json
 .tox/
diff --git a/.goreleaser.yaml b/.goreleaser.yaml
index 061d7acda9..a0d5fff1a9 100644
--- a/.goreleaser.yaml
+++ b/.goreleaser.yaml
@@ -16,8 +16,14 @@ builds:
       - amd64
       - arm64
     main: ./cmd/cog
+    flags:
+      - -trimpath
     ldflags:
-      - "-s -w -X github.com/replicate/cog/pkg/global.Version={{.Version}} -X github.com/replicate/cog/pkg/global.Commit={{.Commit}} -X github.com/replicate/cog/pkg/global.BuildTime={{.Date}}"
+      - -s
+      - -w
+      - -X github.com/replicate/cog/pkg/global.Version={{ if index .Env "COG_VERSION_OVERRIDE"  }}{{ .Env.COG_VERSION_OVERRIDE }}{{ else }}{{ .Version }}{{ end }}
+      - -X github.com/replicate/cog/pkg/global.Commit={{ if index .Env "COG_COMMIT_OVERRIDE"  }}{{ .Env.COG_COMMIT_OVERRIDE }}{{ else }}{{ .Commit }}{{ end }}
+      - -X github.com/replicate/cog/pkg/global.BuildTime={{ .Date }}
   - binary: base-image
     id: base-image
     goos:
@@ -27,8 +33,14 @@ builds:
       - amd64
       - arm64
     main: ./cmd/base-image
+    flags:
+      - -trimpath
     ldflags:
-      - "-s -w -X github.com/replicate/cog/pkg/global.Version={{.Version}} -X github.com/replicate/cog/pkg/global.Commit={{.Commit}} -X github.com/replicate/cog/pkg/global.BuildTime={{.Date}}"
+      - -s
+      - -w
+      - -X github.com/replicate/cog/pkg/global.Version={{ if index .Env "COG_VERSION_OVERRIDE"  }}{{ .Env.COG_VERSION_OVERRIDE }}{{ else }}{{ .Version }}{{ end }}
+      - -X github.com/replicate/cog/pkg/global.Commit={{ if index .Env "COG_COMMIT_OVERRIDE"  }}{{ .Env.COG_COMMIT_OVERRIDE }}{{ else }}{{ .Commit }}{{ end }}
+      - -X github.com/replicate/cog/pkg/global.BuildTime={{ .Date }}
 archives:
   - format: binary
     builds:
diff --git a/Makefile b/Makefile
index 7578904089..ad620a4bfc 100644
--- a/Makefile
+++ b/Makefile
@@ -14,19 +14,8 @@ GORELEASER := $(GO) run github.com/goreleaser/goreleaser/v2@v2.2.0
 PYTHON ?= python
 TOX := $(PYTHON) -Im tox
 
-# If cog's wheel has been prebuilt, it can be specified with the COG_WHEEL
-# environment variable and we will not attempt to build it.
-ifndef COG_WHEEL
-COG_PYTHON_VERSION := $(shell $(PYTHON) -m setuptools_scm 2>/dev/null)
-ifndef COG_PYTHON_VERSION
-$(error Could not determine a version for cog! Did you `pip install -e '.[dev]'` first?)
-endif
-COG_WHEEL := dist/cog-$(COG_PYTHON_VERSION)-py3-none-any.whl
-endif
-
 COG_GO_SOURCE := $(shell find cmd pkg -type f)
 COG_PYTHON_SOURCE := $(shell find python/cog -type f -name '*.py')
-COG_EMBEDDED_WHEEL := pkg/dockerfile/embed/$(notdir $(COG_WHEEL))
 
 COG_BINARIES := cog base-image
 
@@ -36,17 +25,24 @@ default: all
 all: cog
 
 .PHONY: wheel
-wheel: $(COG_EMBEDDED_WHEEL)
+wheel: pkg/dockerfile/embed/.wheel
 
-$(COG_EMBEDDED_WHEEL): $(COG_WHEEL)
+ifdef COG_WHEEL
+pkg/dockerfile/embed/.wheel: $(COG_WHEEL)
 	@mkdir -p pkg/dockerfile/embed
 	@rm -f pkg/dockerfile/embed/*.whl # there can only be one embedded wheel
-	cp $< $@
-
-$(COG_WHEEL): $(COG_PYTHON_SOURCE)
-	$(PYTHON) -m build
+	@echo "Using prebuilt COG_WHEEL $<"
+	cp $< pkg/dockerfile/embed/
+	@touch $@
+else
+pkg/dockerfile/embed/.wheel: $(COG_PYTHON_SOURCE)
+	@mkdir -p pkg/dockerfile/embed
+	@rm -f pkg/dockerfile/embed/*.whl # there can only be one embedded wheel
+	$(PYTHON) -m pip wheel --no-deps --no-binary=:all: --wheel-dir=pkg/dockerfile/embed .
+	@touch $@
+endif
 
-$(COG_BINARIES): $(COG_GO_SOURCE) $(COG_EMBEDDED_WHEEL)
+$(COG_BINARIES): $(COG_GO_SOURCE) pkg/dockerfile/embed/.wheel
 	$(GORELEASER) build --clean --snapshot --single-target --id $@ --output $@
 
 .PHONY: install