This paper presents a new view of Explanation-Based Learning (EBL) of natural language parsing. Rather than employing EBL for specializing parsers by inferring new ones, this paper suggests employing EBL for learning how to reduce ambiguity only partially. The present method consists of an EBL algorithm for learning partial-parsers, and a parsing algorithm which combines partial-parsers with existing ``full-parsers". The learned partial-parsers, implementable as Cascades of Finite State Transducers (CFSTs), recognize and combine constituents efficiently, prohibiting spurious overgeneration. The parsing algorithm combines a learned partial-parser with a given full-parser such that the role of the full-parser is limited to combining the constituents, recognized by the partial-parser, and to recognizing unrecognized portions of the input sentence. Besides the reduction of the parse-space prior to disambiguation, the present method provides a way for refining existing disambiguation models that learn stochastic grammars from tree-banks. We exhibit encouraging empirical results using a pilot implementation: parse-space is reduced substantially with minimal loss of coverage. The speedup gain for disambiguation models is exemplified by experiments with the DOP model.