We study the evolution of T-spline level sets (i.e, implicitly defined T-spline curves and surfaces). The use of T-splines leads to a sparse representation of the geometry and allows for an adaptation to the given data, which can be unorganized points or images. The evolution process is governed by a combination of prescribed, data-driven normal velocities, and additional distance field constraints. By incorporating the distance field constraints we are able to avoid additional branches and singularities of the T-spline level sets without having to use re-initialization steps. Experimental examples are presented to demonstrate the effectiveness of our approach.