Over the past decade convolutional neural networks (CNNs) have become the driving force of an ever-increasing set of applications, achieving state-of-the-art performance. Modern CNN architectures are often composed of many convolutional and some fully connected layers, and have thousands or millions of parameters. CNNs have shown to be effective in the detection of Event-Related Potentials from electroencephalogram (EEG) signals, notably the P300 component which is frequently employed in Brain-Computer Interfaces (BCIs). However, for this task, the increase in detection rates compared to approaches based on human-engineered features has not been as impressive as in other areas and might not justify such a large number of parameters. In this paper, we study the performance of existing CNN architectures with diverse complexities for single-trial within-subject and cross-subject P300 detection on four different datasets. We also proposed SepConv1D, a very simple CNN architecture consisting of a single depthwise separable 1D convolutional layer followed by a fully connected Sigmoid classification neuron. We found that with as few as four filters in its convolutional layer and an overall small number of parameters, SepConv1D obtained competitive performances in the four datasets. We believe these results may represent an important step towards building simpler, cheaper, faster, and more portable BCIs.