Modern systems for automatic speech recognition, including the RNN-Transducer and Attention-based Encoder-Decoder (AED), are designed so that the encoder is not required to alter the time-position of information from the audio sequence into the embedding; alignment to the final text output is processed during decoding. We discover that the transformer-based encoder adopted in recent years is actually capable of performing the alignment internally during the forward pass, prior to decoding. This new phenomenon enables a simpler and more efficient model, the "Aligner-Encoder". To train it, we discard the dynamic programming of RNN-T in favor of the frame-wise cross-entropy loss of AED, while the decoder employs the lighter text-only recurrence of RNN-T without learned cross-attention -- it simply scans embedding frames in order from the beginning, producing one token each until predicting the end-of-message. We conduct experiments demonstrating performance remarkably close to the state of the art, including a special inference configuration enabling long-form recognition. In a representative comparison, we measure the total inference time for our model to be 2x faster than RNN-T and 16x faster than AED. Lastly, we find that the audio-text alignment is clearly visible in the self-attention weights of a certain layer, which could be said to perform "self-transduction".