In such a brief period, the recent coronavirus (COVID-19) already infected large populations worldwide. Diagnosing an infected individual requires a Real-Time Polymerase Chain Reaction (RT-PCR) test, which can become expensive and limited in most developing countries, making them rely on alternatives like Chest X-Rays (CXR) or Computerized Tomography (CT) scans. However, results from these imaging approaches radiated confusion for medical experts due to their similarities with other diseases like pneumonia. Other solutions based on Deep Convolutional Neural Network (DCNN) recently improved and automated the diagnosis of COVID-19 from CXRs and CT scans. However, upon examination, most proposed studies focused primarily on accuracy rather than deployment and reproduction, which may cause them to become difficult to reproduce and implement in locations with inadequate computing resources. Therefore, instead of focusing only on accuracy, this work investigated the effects of parameter reduction through a proposed truncation method and analyzed its effects. Various DCNNs had their architectures truncated, which retained only their initial core block, reducing their parameter sizes to <1 M. Once trained and validated, findings have shown that a DCNN with robust layer aggregations like the InceptionResNetV2 had less vulnerability to the adverse effects of the proposed truncation. The results also showed that from its full-length size of 55 M with 98.67% accuracy, the proposed truncation reduced its parameters to only 441 K and still attained an accuracy of 97.41%, outperforming other studies based on its size to performance ratio.