Recent machine learning based approaches to speech enhancement operate in the time domain and have been shown to outperform the classical enhancement methods. Two such models are SE-GAN and SE-WaveNet, both of which rely on complex neural network architectures, making them expensive to train. We propose using the Variance Constrained Autoencoder (VCAE) for speech enhancement. Our model uses a more straightforward neural network structure than competing solutions and is a natural model for the task of speech enhancement. We demonstrate experimentally that the proposed enhancement model outperforms SE-GAN and SE-WaveNet in terms of perceptual quality of enhanced signals.