Possible Clues:

• Objection's over evidence of smoking, for example
• Torn-off part
• Bump
• Strike (a toe, say) against something hard
• What little remains of naval vessel over time
• Knock (toe); short remnant
• Much-used pencil, e.g.
• One-inch pencil, e.g.
• End of cigarette or counterfoil of cheque
• Injure, as one's 4 Down