In this paper, we aim to provide elements to contribute to the discussion about the usefulness of deep CNNs with several filters to solve both within-subject and cross-subject classification for single-trial P300 detection. To that end, we present SepConv1D, a simple Convolutional Neural Network architecture consisting of a depthwise separable 1D convolutional block followed by a Sigmoid classification block. Additionally, we present a one-layer Fully-Connected Neural Network with two neurons in the hidden layer to show the unnecessary of having complex architectures to solve the problem under analysis. We compare their performances against CNN-based state-of-the-art architectures. The experiments did not show a statistically significant difference between their AUC. Moreover, SepConv1D has the lowest number of parameters of all by far. This is important because simpler, cheaper, faster and, thus, more portable devices can be built.