Computer Tomography (CT) imaging of the chest is a valid diagnosis tool to detect COVID-19 promptly and to control the spread of the disease. In this work we propose a light Convolutional Neural Network (CNN) design, based on the model of the SqueezeNet, for the efficient discrimination of COVID-19 CT images with respect to other community-acquired pneumonia and/or healthy CT images. The architecture allows to an accuracy of 85.03% with an improvement of about 3.2% in the first dataset arrangement and of about 2.1% in the second dataset arrangement. The obtained gain, though of low entity, can be really important in medical diagnosis and, in particular, for Covid-19 scenario. Also the average classification time on a high-end workstation, 1.25 s, is very competitive with respect to that of more complex CNN designs, 13.41 s, witch require pre-processing. The proposed CNN can be executed on medium-end laptop without GPU acceleration in 7.81 s: this is impossible for methods requiring GPU acceleration. The performance of the method can be further improved with efficient pre-processing strategies for witch GPU acceleration is not necessary.