In model-based object recognition and pose estimation, it is common for the set of extracted image features to be much larger than the set of object model features owing to clutter in the image. However, another class of recognition problems has a large model, but only a portion of the object is visible in the image, in which a small set of features can be extracted, most of which are salient. In this case, reducing the effective complexity of the object model is more important than the image clutter. We describe techniques to accomplish this by sampling the space of object positions. A subset of the object model is considered for each sampled pose. This reduces the complexity of the method from cubic to linear in the number of extracted features. We have integrated this technique into a system for recognizing craters on planetary bodies that operates in real-time.