Organic transistors with submicron dimensions have been shown to deviate from the expected behaviour due to a variety of so-called 'short-channel' effects, resulting in nonlinear output characteristics and a lack of current saturation, considerably limiting their use. Here, using an electrochemically-doped polymer in which ions are dynamically injected and removed from the bulk of the semiconductor, we show that devices with nanoscale channel lengths, down to 50 nm, exhibit output curves with well-defined linear and saturation regimes. Additionally, they show very large on-currents on par with their microscale counterparts, large on-to-off ratios of 108, and record-high width-normalised transconductances above 10 S m-1. We believe this work paves the way for the fabrication of high-gain, high-current polymer integrated circuits such as sensor arrays operating at voltages below |1 V| and prepared using simple solution processing methods.