A rotary sub-assembly for pumping of drug fluid in a drug-delivery device, said sub-assembly comprising: a hollow body comprising a housing side wall defining a cavity extending about a longitudinal axis (201, 401, 601) between a closed distal end and an open proximal end, the housing side wall including two ports (226, 228) passing therethrough and in fluid communication with the cavity, wherein at least a working portion of the cavity has a non-circular cross-section extending along a plane perpendicular to the longitudinal axis, the working portion being defined by first inwardly-offset segments (232, 234) of the housing side wall interconnected by second segments (246, 248) of the housing side wall, the first inwardly-offset segments spaced from the longitudinal axis by a constant or varying first radial distance (a), and the second segments spaced from the longitudinal axis by a constant or varying second radial distance (b) that is greater than the first radial distance, wherein said first inwardly-offset segments of the housing side wall are disposed along regions of the side wall surrounding said two ports, and said second segments of the housing side wall are spaced apart from said two ports; and a plunger housed in the cavity and defining a working chamber between the plunger and the housing side wall, wherein: the plunger is configured to rotate relative to the body in order to put the working chamber into sequential fluid-flow communication with one of said two ports (226, 228), then no port, then the other of said two ports, the plunger is further configured to move in longitudinal translation relative to the body and thereby cause a volume of said working chamber to vary in order to successively take in a drug fluid from one of said two ports and then to discharge the fluid from the other of said two ports, and the plunger is sized and shaped such that when the working chamber is in fluid-flow communication with one of said two ports, a side wall of the plunger establishes a liquid-tight seal against the first inwardly-offset segment (232, 234) of the housing side wall surrounding the other port of said two ports, but does not establish a liquid-tight seal with the second segments (246, 248) of the housing side wall. a hollow body comprising a housing side wall defining a cavity extending about a longitudinal axis (201, 401, 601) between a closed distal end and an open proximal end, the housing side wall including two ports (226, 228) passing therethrough and in fluid communication with the cavity, wherein at least a working portion of the cavity has a non-circular cross-section extending along a plane perpendicular to the longitudinal axis, the working portion being defined by first inwardly-offset segments (232, 234) of the housing side wall interconnected by second segments (246, 248) of the housing side wall, the first inwardly-offset segments spaced from the longitudinal axis by a constant or varying first radial distance (a), and the second segments spaced from the longitudinal axis by a constant or varying second radial distance (b) that is greater than the first radial distance, wherein said first inwardly-offset segments of the housing side wall are disposed along regions of the side wall surrounding said two ports, and said second segments of the housing side wall are spaced apart from said two ports; and a plunger housed in the cavity and defining a working chamber between the plunger and the housing side wall, wherein: the plunger is configured to rotate relative to the body in order to put the working chamber into sequential fluid-flow communication with one of said two ports (226, 228), then no port, then the other of said two ports, the plunger is further configured to move in longitudinal translation relative to the body and thereby cause a volume of said working chamber to vary in order to successively take in a drug fluid from one of said two ports and then to discharge the fluid from the other of said two ports, and the plunger is sized and shaped such that when the working chamber is in fluid-flow communication with one of said two ports, a side wall of the plunger establishes a liquid-tight seal against the first inwardly-offset segment (232, 234) of the housing side wall surrounding the other port of said two ports, but does not establish a liquid-tight seal with the second segments (246, 248) of the housing side wall. the plunger is configured to rotate relative to the body in order to put the working chamber into sequential fluid-flow communication with one of said two ports (226, 228), then no port, then the other of said two ports, the plunger is further configured to move in longitudinal translation relative to the body and thereby cause a volume of said working chamber to vary in order to successively take in a drug fluid from one of said two ports and then to discharge the fluid from the other of said two ports, and the plunger is sized and shaped such that when the working chamber is in fluid-flow communication with one of said two ports, a side wall of the plunger establishes a liquid-tight seal against the first inwardly-offset segment (232, 234) of the housing side wall surrounding the other port of said two ports, but does not establish a liquid-tight seal with the second segments (246, 248) of the housing side wall.