Various strategies have been proposed to tabulate complex chemistry for subsequent introduction into fluid mechanics computations. Some of them are grounded on laminar flame calculations, which are useful to seek out key relations linking a few control parameters with relevant species responses. The objective of this paper is to estimate whether approaches based on premixed flamelets (FPI or FGM) can be extended to partially premixed and diffusion flames. Prototypes of nonpremixed laminar and strained counterflow flames are simulated using fully detailed chemistry. The configuration studied is a jet of methane/air mixture opposed to an air stream. A set of reference flames is then obtained, to which FPI results are compared. By varying the equivalence ratio of the free stream of methane/air mixture, from stoichiometry up to pure methane, premixed, partially premixed, and diffusion flames are analyzed. When the fresh fuel/oxidizer mixture equivalence ratio takes values within the flammability limits, excellent results are obtained with FPI. When this equivalence ratio is outside the flammability limits, diffusive fluxes across isomixture fraction surfaces lead to a departure between the FPI tabulation and the reference detailed chemistry flames. This is associated mainly with the appearance of a double-flame structure, progressively evolving into a single diffusion flame when the fuel side equivalence ratio is further increased. Using an improved flame index to distinguish between premixed and diffusion flame burning, hybrid partially premixed combustion is reproduced from a combination of FPI and diffusion flamelets.