A theory of time jitter in semiconductor lasers initially biased just below threshold is developed. Simulations of the buildup of emitted optical pulses in lasers starting from below or above threshold are also presented which, for initial biasing up to threshold, are in good agreement with the theory. In particular, we show that time jitter does not vary for biasing currents up to about 0.95 of the threshold value, while it suffers a small increase at threshold and a steep decrease for higher biasing currents.