Piston face (104, 204, 304) and combustion chamber (18) designs for use particularly in HSDI (high speed direct injection) diesel engines include an open bowl (108, 208, 308) characterized by a large face perimeter region (106, 206, 306) on the piston face (104, 204, 304), and a bowl (18) defined by a first depressed region (112, 212, 312) gently sloping radially inwardly from the face perimeter region (106, 206, 306) and a second depressed region (116, 216, 316) sharply sloping radially inwardly from the first depressed region (112, 212, 312) to the bowl floor (120, 220, 320). Injection is preferably directed towards an intermediate edge which is well-defined between the first and second depressed regions, resulting in portions of the injected fuel plume being directed to both the squish regions and the portion of the bowl situated below the intermediate edge. The designs promote premixed or MK (Modulated Kinetics) combustion, with a concomitant reduction in soot and nitrous oxides (NOx) emissions while maintaining or enhancing brake specific fuel consumption.