Diverse computer-aided diagnosis systems based on convolutional neural networks were applied to automate the detection of myocardial infarction (MI) found in electrocardiogram (ECG) for early diagnosis and prevention. However, issues, particularly overfitting and underfitting, were not being taken into account. In other words, it is unclear whether the network structure is too simple or complex. Toward this end, the proposed models were developed by starting with the simplest structure: a multi-lead features-concatenate narrow network (N-Net) in which only two convolutional layers were included in each lead branch. Additionally, multi-scale features-concatenate networks (MSN-Net) were also implemented where larger features were being extracted through pooling the signals. The best structure was obtained via tuning both the number of filters in the convolutional layers and the number of inputting signal scales. As a result, the N-Net reached a 95.76% accuracy in the MI detection task, whereas the MSN-Net reached an accuracy of 61.82% in the MI locating task. Both networks give a higher average accuracy and a significant difference of p < 0.001 evaluated by the U test compared with the state-of-the-art. The models are also smaller in size thus are suitable to fit in wearable devices for offline monitoring. In conclusion, testing throughout the simple and complex network structure is indispensable. However, the way of dealing with the class imbalance problem and the quality of the extracted features are yet to be discussed.