We investigated whether surface texture (i.e., stochastic roughness) influences softness perception during direct touch interactions with elastic, textured stimuli. Using a Bayesian adaptive modeling approach and a 2AFC task, we evaluated participants' ability to discriminate the softness of stimuli that varied in both their stochastic surface roughness (Hurst exponent) and material elasticity. To explore potential interactions between these features, we conducted two discrimination experiments, testing stimuli from two distinct ranges of elasticity. All participants performed the task using pressing. Results show that softness discrimination was determined primarily by material elasticity, with no discernible influence of surface features. The findings suggest that humans effectively isolate elasticity-based information from smaller-scale surface topography or texture during direct pressing with the finger.