Phone posteriors has recently quite often used (as additional features or as local scores) to improve state-of-the-art automatic speech recognition (ASR) systems. Usually, better phone posterior estimates yield better ASR performance. In the present paper we present some initial, yet promising, work towards hierarchically improving these phone posteriors, by implicitly integrating phonetic and lexical knowledge. In the approach investigated here, phone posteriors estimated with a multilayer perceptron (MLP) and short (9 frames) temporal context, are used as input to a second MLP, spanning a longer temporal context (e.g. 19 frames of posteriors) and trained to refine the phone posterior estimates. The rationale behind this is that at the output of every MLP, the information stream is getting simpler (converging to a sequence of binary posterior vectors), and can thus be further processed (using a simpler classifier) by looking at a larger temporal window. Longer term dependencies can be interpreted as phonetic, sub-lexical and lexical knowledge. The resulting enhanced posteriors can then be used for phone and word recognition, in the same way as regular phone posteriors, in hybrid HMM/ANN or Tandem systems. The proposed method has been tested on TIMIT, OGI Numbers and Conversational Telephone Speech (CTS) databases, always resulting in consistent and significant improvements in both phone and word recognition rates.