In this paper, we propose a residual echo suppression method using a UNet neural network that directly maps the outputs of a linear acoustic echo canceler to the desired signal in the spectral domain. This system embeds a design parameter that allows a tunable tradeoff between the desired-signal distortion and residual echo suppression in double-talk scenarios. The system employs 136 thousand parameters, and requires 1.6 Giga floating-point operations per second and 10 Mega-bytes of memory. The implementation satisfies both the timing requirements of the AEC challenge and the computational and memory limitations of on-device applications. Experiments are conducted with 161 h of data from the AEC challenge database and from real independent recordings. We demonstrate the performance of the proposed system in real-life conditions and compare it with two competing methods regarding echo suppression and desired-signal distortion, generalization to various environments, and robustness to high echo levels.