The assumptions underpinning ancestral state reconstruction are violated in many evolutionary systems, especially for traits under directional selection. However, the accuracy of ancestral state reconstruction for non-neutral traits is poorly understood. To investigate the accuracy of ancestral state reconstruction methods, trees and binary characters were simulated under the BiSSE (Binary State Speciation and Extinction) model using a wide range of character-state-dependent rates of speciation, extinction and character-state transition. We used maximum parsimony (MP), BiSSE and two-state Markov (Mk2) models to reconstruct ancestral states. Under each method, error rates increased with node depth, true number of state transitions, and rates of state transition and extinction; exceeding 30% for the deepest 10% of nodes and highest rates of extinction and character-state transition. Where rates of character-state transition were asymmetrical, error rates were greater when the rate away from the ancestral state was largest. Preferential extinction of species with the ancestral character state also led to higher error rates. BiSSE outperformed Mk2 in all scenarios where either speciation or extinction was state dependent and outperformed MP under most conditions. MP outperformed Mk2 in most scenarios except when the rates of character-state transition and/or extinction were highly asymmetrical and the ancestral state was unfavoured.