We develop neural morphological tagging and disambiguation models for Estonian. First, we experiment with two neural architectures for morphological tagging – a standard multiclass classifier which treats each morphological tag as a single unit, and a sequence model which handles the morphological tags as sequences of morphological category values. Secondly, we complement these models with the analyses generated by a rule-based Estonian morphological analyser (MA) VABAMORF, thus performing a soft morphological disambiguation. We compare two ways of supplementing a neural morphological tagger with the MA outputs: firstly, by adding the combined analyses embeddings to the word representation input to the neural tagging model, and secondly, by adopting an attention mechanism to focus on the most relevant analyses generated by the MA. Experiments on three Estonian datasets show that our neural architectures consistently outperform the non-neural baselines, including HMM-disambiguated VABAMORF, while augmenting models with MA outputs results in a further performance boost for both models.