A field-effect semiconductor device, for example a MOSFET of the trench-gate type, comprises side-by-side device cells at a surface (10a) of a semiconductor body (10), and at least one drain connection (41) that extends in a drain trench (40) from the body surface (10a) to an underlying drain region (14a). A channel-accommodating region (15) of the device extends laterally to the drain trench (40). The drain trench (40) extends through the thickness of the channel-accommodating region (15) to the underlying drain region (14a), and the drain connection (41) is separated from the channel-accommodating region (15) by an intermediate insulating layer (24) on side-walls of the drain trench (40). A compact cellular layout can be achieved, with a significant proportion of the total cellular layout area accommodating conduction channels (12). The configuration in a discrete device avoids a need to use a substrate conduction path and so advantageously reduces the ON resistance of the device.