diff --git a/cibuildwheel/resources/constraints-python310.txt b/cibuildwheel/resources/constraints-python310.txt
index 40cad0dd1..0600b10e0 100644
--- a/cibuildwheel/resources/constraints-python310.txt
+++ b/cibuildwheel/resources/constraints-python310.txt
@@ -1,5 +1,5 @@
 # This file was autogenerated by uv via the following command:
-#    uv pip compile --python-version=3.10 cibuildwheel/resources/constraints.in --output-file=cibuildwheel/resources/constraints-python310.txt
+#    nox -s update_constraints
 build==1.1.1
 delocate==0.10.7
 distlib==0.3.8
diff --git a/cibuildwheel/resources/constraints-python311.txt b/cibuildwheel/resources/constraints-python311.txt
index 9ee04f989..d8a5a79f7 100644
--- a/cibuildwheel/resources/constraints-python311.txt
+++ b/cibuildwheel/resources/constraints-python311.txt
@@ -1,5 +1,5 @@
 # This file was autogenerated by uv via the following command:
-#    uv pip compile --python-version=3.11 cibuildwheel/resources/constraints.in --output-file=cibuildwheel/resources/constraints-python311.txt
+#    nox -s update_constraints
 build==1.1.1
 delocate==0.10.7
 distlib==0.3.8
diff --git a/cibuildwheel/resources/constraints-python312.txt b/cibuildwheel/resources/constraints-python312.txt
index 6dc1d894f..d8a5a79f7 100644
--- a/cibuildwheel/resources/constraints-python312.txt
+++ b/cibuildwheel/resources/constraints-python312.txt
@@ -1,5 +1,5 @@
 # This file was autogenerated by uv via the following command:
-#    uv pip compile --python-version=3.12 cibuildwheel/resources/constraints.in --output-file=cibuildwheel/resources/constraints-python312.txt
+#    nox -s update_constraints
 build==1.1.1
 delocate==0.10.7
 distlib==0.3.8
diff --git a/cibuildwheel/resources/constraints-python37.txt b/cibuildwheel/resources/constraints-python37.txt
index d9cd8fb39..273c799f5 100644
--- a/cibuildwheel/resources/constraints-python37.txt
+++ b/cibuildwheel/resources/constraints-python37.txt
@@ -1,5 +1,5 @@
 # This file was autogenerated by uv via the following command:
-#    uv pip compile --python-version=3.7 cibuildwheel/resources/constraints.in --output-file=cibuildwheel/resources/constraints-python37.txt
+#    nox -s update_constraints
 build==1.1.1
 delocate==0.10.7
 distlib==0.3.8
diff --git a/cibuildwheel/resources/constraints-python38.txt b/cibuildwheel/resources/constraints-python38.txt
index c6ac13df6..0600b10e0 100644
--- a/cibuildwheel/resources/constraints-python38.txt
+++ b/cibuildwheel/resources/constraints-python38.txt
@@ -1,5 +1,5 @@
 # This file was autogenerated by uv via the following command:
-#    uv pip compile --python-version=3.8 cibuildwheel/resources/constraints.in --output-file=cibuildwheel/resources/constraints-python38.txt
+#    nox -s update_constraints
 build==1.1.1
 delocate==0.10.7
 distlib==0.3.8
diff --git a/cibuildwheel/resources/constraints-python39.txt b/cibuildwheel/resources/constraints-python39.txt
index 48a239beb..0600b10e0 100644
--- a/cibuildwheel/resources/constraints-python39.txt
+++ b/cibuildwheel/resources/constraints-python39.txt
@@ -1,5 +1,5 @@
 # This file was autogenerated by uv via the following command:
-#    uv pip compile --python-version=3.9 cibuildwheel/resources/constraints.in --output-file=cibuildwheel/resources/constraints-python39.txt
+#    nox -s update_constraints
 build==1.1.1
 delocate==0.10.7
 distlib==0.3.8
diff --git a/cibuildwheel/resources/constraints.txt b/cibuildwheel/resources/constraints.txt
index 6dc1d894f..d8a5a79f7 100644
--- a/cibuildwheel/resources/constraints.txt
+++ b/cibuildwheel/resources/constraints.txt
@@ -1,5 +1,5 @@
 # This file was autogenerated by uv via the following command:
-#    uv pip compile --python-version=3.12 cibuildwheel/resources/constraints.in --output-file=cibuildwheel/resources/constraints-python312.txt
+#    nox -s update_constraints
 build==1.1.1
 delocate==0.10.7
 distlib==0.3.8
diff --git a/noxfile.py b/noxfile.py
index 9748a8cf3..19dbed42b 100644
--- a/noxfile.py
+++ b/noxfile.py
@@ -66,14 +66,14 @@ def update_constraints(session: nox.Session) -> None:
     """
 
     if getattr(session.virtualenv, "venv_backend", "") != "uv":
-        session.install("uv")
+        session.install("uv>=0.1.23")
 
     for minor_version in range(7, 13):
         python_version = f"3.{minor_version}"
         env = os.environ.copy()
         # CUSTOM_COMPILE_COMMAND is a pip-compile option that tells users how to
         # regenerate the constraints files
-        env["CUSTOM_COMPILE_COMMAND"] = f"nox -s {session.name}"
+        env["UV_CUSTOM_COMPILE_COMMAND"] = f"nox -s {session.name}"
         session.run(
             "uv",
             "pip",