diff --git a/web/fup/fuphttp/fngen/fngen.go b/web/fup/fuphttp/fngen/fngen.go
index 9828bd69cf..647bdce4e3 100644
--- a/web/fup/fuphttp/fngen/fngen.go
+++ b/web/fup/fuphttp/fngen/fngen.go
@@ -63,7 +63,8 @@ func BoringGenerator(filenamePrefix string, filenameExt string, attempt int) str
 	return string(out)
 }
 
-func uniqueName(ctx context.Context, existsFn func(ctx context.Context, name string) (bool, error), filenamePrefix, extension string, generator FilenameGenerator) (string, error) {
+// UniqueName repeatedly attempts to generate a name until existsFn returns false.
+func UniqueName(ctx context.Context, existsFn func(ctx context.Context, name string) (bool, error), filenamePrefix, extension string, generator FilenameGenerator) (string, error) {
 	// There's a race condition here, because we might generate a currently-not-taken filename and collide with someone uploading with the same name.
 	// However, given the usecase of this software, I've decided not to care. I'm unlikely to be uploading enough things concurrently that this is a real issue.
 	attempt := 0
diff --git a/web/fup/fuphttp/fngen/fngen_test.go b/web/fup/fuphttp/fngen/fngen_test.go
index b2e9abf1c1..0678533a0c 100644
--- a/web/fup/fuphttp/fngen/fngen_test.go
+++ b/web/fup/fuphttp/fngen/fngen_test.go
@@ -5,6 +5,7 @@
 package fngen_test
 
 import (
+	"context"
 	"fmt"
 	"strings"
 	"testing"
@@ -47,3 +48,49 @@ func TestBoringGenerator(t *testing.T) {
 		t.Errorf("BoringGenerator(%q, %q, 0) = %q; want something ending in %v", "prefix", ".ext", got, ".ext")
 	}
 }
+
+func TestUniqueName(t *testing.T) {
+	gen := func(filenamePrefix string, filenameExt string, attempt int) string {
+		return fmt.Sprintf("%s.%d%s", filenamePrefix, attempt, filenameExt)
+	}
+	exists := func(ctx context.Context, name string) (bool, error) {
+		switch name {
+		case "firstTry.0.txt":
+			return false, nil
+		case "secondTry.0.txt":
+			return true, nil
+		case "secondTry.1.txt":
+			return false, nil
+		default:
+			return false, fmt.Errorf("no existence recorded for %q for testing", name)
+		}
+	}
+
+	ctx := context.Background()
+	tcs := []struct {
+		prefix  string
+		want    string
+		wantErr bool
+	}{{
+		prefix: "firstTry",
+		want:   "firstTry.0.txt",
+	}, {
+		prefix: "secondTry",
+		want:   "secondTry.1.txt",
+	}, {
+		prefix:  "error",
+		wantErr: true,
+	}}
+	for _, tc := range tcs {
+		got, err := fngen.UniqueName(ctx, exists, tc.prefix, ".txt", gen)
+		switch {
+		case err != nil && !tc.wantErr:
+			t.Errorf("UniqueName(%q): %v", tc.prefix, err)
+		case err == nil && tc.wantErr:
+			t.Errorf("UniqueName(%q) didn't return error; expected one", tc.prefix)
+		}
+		if got != tc.want {
+			t.Errorf("UniqueName(%q) = %q; want %q", tc.prefix, got, tc.want)
+		}
+	}
+}