Haplotype data play a relevant role in several genetic studies, e.g., mapping of complex disease genes, drug design, and evolutionary studies on populations. However, the experimental determination of haplotypes is expensive and time-consuming. This motivates the increasing interest in techniques for inferring haplotype data from genotypes, which can instead be obtained quickly and economically. Several such techniques are based on the maximum parsimony principle, which has been justified by both experimental results and theoretical arguments. However, the problem of haplotype inference by parsimony was shown to be NP-hard, thus limiting the applicability of exact parsimony-based techniques to relatively small data sets. In this paper, we introduce collapse rule, a generalization of the well-known Clark's rule, and describe a new heuristic algorithm for haplotype inference (implemented in a program called CollHaps), based on parsimony and the iterative application of collapse rules. The performance of CollHaps is tested on several data sets. The experiments show that CollHaps enables the user to process large data sets obtaining very "parsimonious" solutions in short processing times. They also show a correlation, especially for large data sets, between parsimony and correct reconstruction, supporting the validity of the parsimony principle to produce accurate solutions.