Data-driven methods have received increasing attention in recent years in order to meet real-time requirements in computationally intensive tasks. In our current work we examine the application of such approaches in soft-tissue simulation. The core idea is to split deformations into a coarse approximation and a differential part that contains the details. We employ the data-driven stamping approach to enrich a fast simulation surface with details that have been extracted from a set of example deformations obtained in offline computations. In this paper we detail our technique, and suggest further extensions over our previous work. First, we propose an improved method for correlating the current coarse approximation to the examples in the database. The new correlation metric combines Euclidean distances with cosine similarity. It allows for better example discrimination, resulting in a well-conditioned linear system. This also enables us to use a non-negative least squares solver that leads to a better regression and guarantees positive stamp blending weights. Second, we suggest a frequency-space stamp compression scheme that saves memory and, in most instances, is faster, since many operations can be done in the compressed space. Third, cutting is included by employing a physically-inspired influence map that allows for proper handling of material discontinuities that were not present in the original examples. We thoroughly evaluate our method and demonstrate its practical application in a surgical simulator prototype.