How do T Tauri stars accrete?

We conjecture that observed protoplanetary disc accretion rates may be explained with low viscosities, which could be the result of hydrodynamic turbulence. We show that viscosities parametrized in the usual way with alpha greater than or similar to 10(-4), comparable to values suggested for hydrodynamic turbulence, can explain the observed accretion rates and lifetimes with plausible inner disc surface densities. Our models are also in better agreement with surface density estimates of the minimum mass solar nebula than models with rapid transport for a given mass accretion rate, such as recent models of accretion driven by magnetic winds. The required surface densities are a natural result of the protostellar infall phase, as long as non-gravitational transport is limited. We argue that, in addition to possible non-ideal magnetic transport due to disc winds possibly modified by the Hall effect, the effects of low-viscosity hydrodynamic accretion deserve more consideration.