A water redispersible polymer powder is produced by drying an aqueous mixture of a high Tg carboxylated styrene butadiene polymer and a low Tg carboxylated styrene butadiene polymer, where the ratio of the mean or average particle size of the high Tg polymer to the particle size of the low Tg polymer is from 1:1 to 5:1, preferably from 1:1 to 3:1, and the amount of the high Tg polymer is from 20 wt. % to 35 wt. %, preferably from 25 wt. % to 30 wt. %, based upon the total weight of the high Tg polymer and the low Tg polymer. Cement compositions such as mortars, which contain the redispersible polymer powder exhibit unexpectedly superior high bond strength and high impact resistance.