Height fields and depth maps which we collectively refer to as z-fields, usually carry a lot of redundant information and are often used in real-time applications. This is the reason why efficient methods for their simplification are necessary. On the other hand, the computation power and programmability of commodity graphics hardware has significantly grown. We present an adaptation of an existing real-time z-field simplification method for execution in graphics hardware. The main parts of the algorithm are implemented as fragment programs which run on the GPU. The resulting polygonal models are identical to the ones obtained by the original method. The main benefit is that the computation load is imposed on the GPU, freeing-up the CPU for other tasks. Additionally, the new method exhibits a performance improvement when compared to a pure CPU implementation.