diff --git a/backend/archive/zip/zip.go b/backend/archive/zip/zip.go
index 6349807b1..129ce010e 100644
--- a/backend/archive/zip/zip.go
+++ b/backend/archive/zip/zip.go
@@ -145,6 +145,13 @@ func (f *Fs) readZip() (singleObject bool, err error) {
 			skipped++
 			continue
 		}
+		isDir := strings.HasSuffix(file.Name, "/")
+		// A file entry whose last component is "", "." or ".." names
+		// a directory rather than a file, so skip
+		if !isDir && sanitize.Leaf(path.Base(file.Name)) != nil {
+			skipped++
+			continue
+		}
 		remote = path.Join(f.prefix, remote)
 		if f.root != "" {
 			// Ignore all files outside the root, requiring a path
@@ -159,19 +166,12 @@ func (f *Fs) readZip() (singleObject bool, err error) {
 				remote = strings.TrimPrefix(remote, f.root+"/")
 			}
 		}
-		if strings.HasSuffix(file.Name, "/") {
+		if isDir {
 			dir := fs.NewDir(remote, file.Modified)
 			dt.AddDir(dir)
 		} else {
 			if remote == "" {
-				// A file at the root itself can only be the
-				// archive member f.root points at - with no root
-				// it is a crafted name for the archive's own
-				// directory, which can't be a file
-				if f.root == "" {
-					skipped++
-					continue
-				}
+				// A file at the root is the archive member f.root points at
 				remote = path.Base(f.root)
 				singleObject = true
 				dt = dirtree.New()
diff --git a/backend/archive/zip/zip_internal_test.go b/backend/archive/zip/zip_internal_test.go
index d13bb9140..6aff03cd5 100644
--- a/backend/archive/zip/zip_internal_test.go
+++ b/backend/archive/zip/zip_internal_test.go
@@ -4,6 +4,7 @@ import (
 	"archive/zip"
 	"bytes"
 	"context"
+	"fmt"
 	"os"
 	"path/filepath"
 	"sort"
@@ -105,10 +106,12 @@ func TestReadZipRootBoundary(t *testing.T) {
 	assert.Equal(t, []string{"a.txt"}, remotes)
 }
 
-// A file entry whose name refers to the archive's own root (".", "/",
-// "./" or "") must be skipped, not turn the whole archive into a single
-// file which hides every other entry.
-func TestReadZipRootNamedEntry(t *testing.T) {
+// A file entry whose name refers to a directory (".", "/", "./", "" or
+// "sub/.") must be skipped, not turn the archive or the directory
+// mounted as its root into a single file which hides every other
+// entry, or become an object named for the archive itself when the
+// archive is found by listing its directory.
+func TestReadZipDirNamedFileEntry(t *testing.T) {
 	ctx := context.Background()
 	dir := t.TempDir()
 	name := writeZip(t, dir, "dot.zip",
@@ -117,16 +120,28 @@ func TestReadZipRootNamedEntry(t *testing.T) {
 		"./",
 		"",
 		"good.txt",
+		"sub/",
+		"sub/.",
+		"sub/good.txt",
 	)
 
 	localFs, err := cache.Get(ctx, dir)
 	require.NoError(t, err)
 
-	f, err := New(ctx, localFs, name, "", "")
-	require.NoError(t, err)
-
-	remotes := allRemotes(t, f)
-	assert.Equal(t, []string{"good.txt"}, remotes)
+	for _, test := range []struct {
+		prefix, root string
+		want         []string
+	}{
+		{"", "", []string{"good.txt", "sub/good.txt"}},
+		{"sub/dot.zip", "", []string{"sub/dot.zip/good.txt", "sub/dot.zip/sub/good.txt"}},
+		{"", "sub", []string{"good.txt"}},
+	} {
+		t.Run(fmt.Sprintf("prefix=%q,root=%q", test.prefix, test.root), func(t *testing.T) {
+			f, err := New(ctx, localFs, name, test.prefix, test.root)
+			require.NoError(t, err)
+			assert.Equal(t, test.want, allRemotes(t, f))
+		})
+	}
 }
 
 // Listings are served from a cache which must survive callers