diff --git a/.circleci/config.yml b/.circleci/config.yml
index ea3d50de5..dd877ca7f 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -449,6 +449,7 @@ jobs:
 
     environment:
       NIX_PATH: "nixpkgs=https://github.com/NixOS/nixpkgs-channels/archive/nixos-19.09-small.tar.gz"
+      SOURCE: "nix/"
 
     steps:
       - "checkout"
@@ -465,7 +466,7 @@ jobs:
             # build a couple simple little dependencies that don't take
             # advantage of multiple cores and we get a little speedup by doing
             # them in parallel.
-            nix-build --cores 3 --max-jobs 2 nix/
+            nix-build --cores 3 --max-jobs 2 "$SOURCE"
 
   nixos-21-05:
     <<: *NIXOS
@@ -474,7 +475,8 @@ jobs:
       # Note this doesn't look more similar to the 19.09 NIX_PATH URL because
       # there was some internal shuffling by the NixOS project about how they
       # publish stable revisions.
-      NIX_PATH: "nixpkgs=https://github.com/NixOS/nixpkgs/archive/refs/heads/nixos-21.05-small.tar.gz"
+      NIX_PATH: "nixpkgs=https://github.com/NixOS/nixpkgs/archive/refs/d32b07e6df276d78e3640eb43882b80c9b2b3459.tar.gz"
+      SOURCE: "nix/py3.nix"
 
   typechecks:
     docker:
diff --git a/nix/overlays.nix b/nix/overlays.nix
index f5ef72cc0..fbd0ce3bb 100644
--- a/nix/overlays.nix
+++ b/nix/overlays.nix
@@ -23,4 +23,11 @@ self: super: {
       collections-extended = python-super.pythonPackages.callPackage ./collections-extended.nix { };
     };
   };
+
+  python39 = super.python39.override {
+    packageOverrides = python-self: python-super: {
+      # collections-extended is not part of nixpkgs at this time.
+      collections-extended = python-super.pythonPackages.callPackage ./collections-extended.nix { };
+    };
+  };
 }
diff --git a/nix/py3.nix b/nix/py3.nix
new file mode 100644
index 000000000..34ede49dd
--- /dev/null
+++ b/nix/py3.nix
@@ -0,0 +1,7 @@
+# This is the main entrypoint for the Tahoe-LAFS derivation.
+{ pkgs ? import <nixpkgs> { } }:
+# Add our Python packages to nixpkgs to simplify the expression for the
+# Tahoe-LAFS derivation.
+let pkgs' = pkgs.extend (import ./overlays.nix);
+# Evaluate the expression for our Tahoe-LAFS derivation.
+in pkgs'.python39.pkgs.callPackage ./tahoe-lafs.nix { }