Conditions for ignoring early exercise

Under what conditions is it safe to value an American call as if it were European? And an American put?

Call: whenever the underlying pays no dividends (and rates are non-negative). Put: essentially only when rates are zero or negative. Exercising a call early gives up time value and the interest on the strike, which is never optimal without dividends. For a put, early exercise lets you earn interest on $K$ sooner, so with positive rates a deep in-the-money American put is worth more than its European twin.