In this paper we introduce a new approach to controlling error in hierarchical clustering algorithms for radiosity. The new method provides control mechanisms which attempt to ensure that just enough work is done to meet the user's quality criteria. To this end the importance of traditionally ignored visibility error is identified, and the concept of {\it features} is introduced as a way to evaluate the quality of an image. A methodology to evaluate error based on features is presented, which leads to the development of a {\it multi-resolution visibility} algorithm. An algorithm to construct a suitable hierarchy for clustering and multi-resolution visibility is also proposed. Results of the implementation show that the multi-resolution approach has the potential of providing significant computational savings depending on the choice of feature size the user is interested in. They also illustrate the relevance of the feature-based error analysis. The proposed algorithms are well suited to the development of interactive lighting simulation systems since they allow more user control. Two additional mechanisms to control the quality of a simulation are presented: The evaluation of internal visibility in a cluster produces more accurate solutions for a given error bound; A progressive multi-gridding approach is introduced for hierarchical radiosity, allowing continuous refinement of a solution in an interactive session.