A two-stroke cycle, compression ignition, opposed-piston engine including at least one cylinder with a bore, piston-controlled exhaust and intake ports near respective ends of the cylinder, and a pair of pistons disposed in opposition in the bore, each piston comprising: a flat end surface with an elongated, concave bowl formed therein to define a combustion chamber with an elongated bowl formed in a flat end surface of an opposing piston; wherein the flat end surface meeting a piston sidewall at a peripheral edge having a circular shape that is centered on a longitudinal axis of the piston and that is disposed at a single longitudinal level of the piston; a pair of notches formed in the end surface and positioned in opposition on the peripheral edge, in alignment with an end surface diameter; the concave bowl having an oblong shape that is elongated along the end surface diameter, between the notches; the concave bowl being flanked on either side by flat end surface portions (108a and 108b) that extend to the peripheral edge; the concave bowl having opposing sidewalls (123 and 124) and a curved bottom portion which connects the sidewalls smoothly in a vertical section; and, a maximum depth (D max) of the bowl being the maximum distance between the curved bottom portion and an end surface plane (P ES), the plane (P ES) intersecting the piston longitudinal axis and being positioned at the single longitudinal level, the maximum depth (D max) of the bowl being offset in an orthogonal direction from a longitudinal cut plane (P L), the plane (P L) containing the piston's longitudinal axis and the diameter, the planes (P L) and (P ES) being mutually orthogonal, the engine further including a combustion chamber with an elongated, rotationally skewed shape formed between the flat end surfaces of the pistons when the pistons are near top center locations in the bore; two fuel injectors disposed in diametrical opposition and in alignment with a centerline of the combustion chamber; in a first longitudinal section, the combustion chamber having a rotationally skewed shape that is symmetrical with respect to the combustion chamber centerline; and, in a second longitudinal section that is orthogonal to the first longitudinal section, the combustion chamber having an elongated shape with opposite end portions that taper along the combustion chamber centerline toward the fuel injectors. a flat end surface with an elongated, concave bowl formed therein to define a combustion chamber with an elongated bowl formed in a flat end surface of an opposing piston; wherein the flat end surface meeting a piston sidewall at a peripheral edge having a circular shape that is centered on a longitudinal axis of the piston and that is disposed at a single longitudinal level of the piston; a pair of notches formed in the end surface and positioned in opposition on the peripheral edge, in alignment with an end surface diameter; the concave bowl having an oblong shape that is elongated along the end surface diameter, between the notches; the concave bowl being flanked on either side by flat end surface portions (108a and 108b) that extend to the peripheral edge; the concave bowl having opposing sidewalls (123 and 124) and a curved bottom portion which connects the sidewalls smoothly in a vertical section; and, a maximum depth (D max) of the bowl being the maximum distance between the curved bottom portion and an end surface plane (P ES), the plane (P ES) intersecting the piston longitudinal axis and being positioned at the single longitudinal level, the maximum depth (D max) of the bowl being offset in an orthogonal direction from a longitudinal cut plane (P L), the plane (P L) containing the piston's longitudinal axis and the diameter, the planes (P L) and (P ES) being mutually orthogonal, the engine further including a combustion chamber with an elongated, rotationally skewed shape formed between the flat end surfaces of the pistons when the pistons are near top center locations in the bore; two fuel injectors disposed in diametrical opposition and in alignment with a centerline of the combustion chamber; in a first longitudinal section, the combustion chamber having a rotationally skewed shape that is symmetrical with respect to the combustion chamber centerline; and, in a second longitudinal section that is orthogonal to the first longitudinal section, the combustion chamber having an elongated shape with opposite end portions that taper along the combustion chamber centerline toward the fuel injectors.