diff --git a/cli/command/image/tree.go b/cli/command/image/tree.go
index 6616e9e207a1..d56cf560e7f8 100644
--- a/cli/command/image/tree.go
+++ b/cli/command/image/tree.go
@@ -206,30 +206,38 @@ var allChips = []imageChip{
 	chipInUse,
 }
 
+// getPossibleChips returns the list of chips used by at least one image.
+// It is used to determine which columns to print (and how much width to
+// reserve).
 func getPossibleChips(view treeView) (chips []imageChip) {
-	remaining := make([]imageChip, len(allChips))
-	copy(remaining, allChips)
+	remaining := slices.Clone(allChips)
+
+	check := func(d imageDetails) (done bool) {
+		// filter without allocating
+		out := remaining[:0]
+		for _, chip := range remaining {
+			if chip.check(&d) {
+				chips = append(chips, chip)
+				continue
+			}
+			out = append(out, chip)
+		}
+		remaining = out
+		return len(remaining) == 0
+	}
 
-	var possible []imageChip
 	for _, img := range view.images {
-		details := []imageDetails{img.Details}
-
-		for _, c := range img.Children {
-			details = append(details, c.Details)
+		if check(img.Details) {
+			return chips
 		}
-
-		for _, d := range details {
-			for idx := len(remaining) - 1; idx >= 0; idx-- {
-				chip := remaining[idx]
-				if chip.check(&d) {
-					possible = append(possible, chip)
-					remaining = append(remaining[:idx], remaining[idx+1:]...)
-				}
+		for _, c := range img.Children {
+			if check(c.Details) {
+				return chips
 			}
 		}
 	}
 
-	return possible
+	return chips
 }
 
 func printImageTree(outs command.Streams, view treeView) {