The dissertation addresses the design of parsing grammars for automatic surface-syntactic analysis of unconstrained English text. It consists of a summary and three articles. {\it Morphological disambiguation} documents a grammar for morphological (or part-of-speech) disambiguation of English, done within the Constraint Grammar framework proposed by Fred Karlsson. The disambiguator seeks to discard those of the alternative morphological analyses proposed by the lexical analyser that are contextually illegitimate. The 1,100 constraints express some 23 general, essentially syntactic statements as restrictions on the linear order of morphological tags. The error rate of the morphological disambiguator is about ten times smaller than that of another state-of-the-art probabilistic disambiguator, given that both are allowed to leave some of the hardest ambiguities unresolved. This accuracy suggests the viability of the grammar-based approach to natural language parsing, thus also contributing to the more general debate concerning the viability of probabilistic vs.\ linguistic techniques. {\it Experiments with heuristics} addresses the question of how to resolve those ambiguities that survive the morphological disambiguator. Two approaches are presented and empirically evaluated: (i) heuristic disambiguation constraints and (ii) techniques for learning from the fully disambiguated part of the corpus and then applying this information to resolving remaining ambiguities.