Stationary states in KPZ-type growth have interesting short distance properties. We find that typically they are skewed and lack particle-hole symmetry. For example, hill-tops are typically flatter than valley-bottoms, and all odd moments of the height distribution function are non-zero. Stationary-state skewness can be turned on and off in the (1 + 1)-dimensional restricted solid-on-solid (RSOS) model. We construct the exact stationary state for its master equation in a four-dimensional parameter space. In this state steps are completely uncorrelated. Familiar models such as the Kim - Kosterlitz model lie outside this space, and their stationary states are skewed. We demonstrate using finite size scaling that the skewness diverges with systems size, but such that the skewness operator is irrelevant in (1 + 1) dimensions, with an exponent , and that the KPZ fixed point lies at zero-skewness.