This paper investigates how automatic quality assessment of spoken language translation (SLT), also named confidence estimation (CE), can help re-decoding SLT output graphs and improve the overall speech translation performance. Our graph redecoding method can be seen as a second-pass of translation. For this, a robust word confidence estimator for SLT is required. We propose several estimators based on our estimation of transcription (ASR) quality, translation (MT) quality, or both (combined ASR+MT). Using these word confidence measures to re-decode the spoken language translation graph leads to a significant BLEU improvement (more than 2 points) compared to our SLT baseline, for a French-English SLT task. These results could be applied to interactive speech translation or computer-assisted translation of speeches and lectures.