  We introduce an iteration of forcing notions satisfying the countable chain
condition with minimal damage to a strong coloring. Applying this method, we
prove that Martin's axiom is strictly stronger than its restriction to forcing
notions satisfying the countable chain condition in all finite powers. Our
method shows also the finer distinction, that Martin's axiom is strictly
stronger than its restriction to forcing notions whose squares satisfy the
countable chain condition.
