Carbon nanotube field-effect transistors are strong candidates in replacing or supplementing silicon technology. Although theoretical studies have projected that nanotube transistors will perform well at nanoscale device dimensions, most experimental studies have been carried out on devices that are about ten times larger than current silicon transistors. Here, we show that nanotube transistors maintain their performance as their channel length is scaled from 3 µm to 15 nm, with an absence of so-called short-channel effects. The 15-nm device has the shortest channel length and highest room-temperature conductance (0.7G₀) and transconductance (40 µS) of any nanotube transistor reported to date. We also show the first experimental evidence that nanotube device performance depends significantly on contact length, in contrast to some previous reports. Data for both channel and contact length scaling were gathered by constructing multiple devices on a single carbon nanotube. Finally, we demonstrate the performance of a nanotube transistor with channel and contact lengths of 20 nm, an on-current of 10 µA, an on/off current ratio of 1 x 10⁵, and peak transconductance of 20 µS. These results provide an experimental forecast for carbon nanotube device performance at dimensions suitable for future transistor technology nodes.