We report on the detection of two Hα-emitting extremely compact objects from deep images of the A634 and A539 clusters of galaxies at z~0.03. Follow-up long-slit spectroscopy of these two unresolved sources revealed that they are members of their respective clusters, showing H II-type spectra. The luminosity and the extreme equivalent width of Hα + [N II] measured for these sources, together with their very compact appearance, has raised a question about the origin of these intense starbursts in the cluster environment. We propose that the compact starburst in A539 resulted from the compression of the interstellar gas of a dwarf galaxy when entering the cluster core, while the starburst galaxy in A634 is likely to be the result of a galaxy-galaxy interaction, illustrating the preprocessing of galaxies during their infall toward the central regions of clusters. The contribution of these compact star-forming dwarf galaxies to the star formation history of galaxy clusters is discussed, as well as a possible link with the recently discovered early-type ultracompact dwarf galaxies. We note that these extreme objects will rarely be detected in normal magnitude-limited optical or NIR surveys, mainly due to their low stellar masses (on the order of 106 Msolar), whereas they will easily show up in dedicated Hα surveys given the high equivalent width of their emission lines.