Process for making organic solvent-free aqueous crosslinkable polymer composition comprising: a) preparing an aqueous solution of an acid-functional oligomer with Tg 10 to 125.degree. C. and having crosslinker functional groups; b) conducting an aqueous emulsion polymerization to make an aqueous emulsion of an olefinic hydrophobic polymer in the presence of the aqueous oligomer solution, the hydrophobic polymer having Tg at least 25.degree. C. below that of the oligomer and optionally crosslinker functional groups, and c) combining with a crosslinking agent reactable with the crosslinker groups of the oligomer and polymer, said composition having Koenig hardness of .gtoreq.40 sec and minimum film forming temperature (MFFT) .ltoreq.55.degree. C. Also the aqueous composition so formed and its use in various applications. The aqueous composition has excellent properties and in particular an advantageous balance of MFFT and Koenig hardness.