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The control flow graph (CFG) representation of a procedure used by virtually all flow-sensitive program analyses, admits a large number of infeasible control flow paths i.e., these paths do not occur in any execution of the program. Hence the information reaching along infeasible paths in an analysis is spurious. This affects the precision of the conventional maximum fixed point (MFP) solution of the data flow analysis, because it includes the information reaching along all control flow paths. The existing approaches for removing this imprecision are either specific to a data flow problem with no straightforward generalization or involve control flow graph restructuring which may exponentially blow up the size of the CFG. We lift the notion of MFP solution to define the notion of feasible path MFP (FPMFP) solutions that exclude the data flowing along known infeasible paths. The notion of FPMFP is generic and does not involve CFG restructuring. Instead, it takes externally supplied information about infeasible paths and lifts any data flow analysis to an analysis that maintains the distinctions between different paths where these distinctions are beneficial, and ignores them where they are not. Thus it gets the benefit of a path-sensitive analysis where it is useful without performing a conventional path-sensitive analysis. We evaluated the proposed feasible path MFP solutions for reaching definitions analysis and potentially uninitialized variable analysis on 30 benchmarks. The evaluation results indicate that precision improvement in these two analyses respectively reduce the number def-use pairs by up to 13.6% (average 2.87%, geometric mean 1.75%), and reduce the potentially uninitialized variable alarms by up to 100% (average 18.5%, geo. mean 3%). We found that the FPMFP computation time was 2.9X of MFP computation time on average.