Intestinal parasites are responsible for several diseases in human beings. In order to eliminate the error-prone visual analysis of optical microscopy slides, we have investigated automated, fast, and low-cost systems for the diagnosis of human intestinal parasites. In this work, we present a hybrid approach that combines the opinion of two decision-making systems with complementary properties: ($DS_1$) a simpler system based on very fast handcrafted image feature extraction and support vector machine classification and ($DS_2$) a more complex system based on a deep neural network, Vgg-16, for image feature extraction and classification. $DS_1$ is much faster than $DS_2$, but it is less accurate than $DS_2$. Fortunately, the errors of $DS_1$ are not the same of $DS_2$. During training, we use a validation set to learn the probabilities of misclassification by $DS_1$ on each class based on its confidence values. When $DS_1$ quickly classifies all images from a microscopy slide, the method selects a number of images with higher chances of misclassification for characterization and reclassification by $DS_2$. Our hybrid system can improve the overall effectiveness without compromising efficiency, being suitable for the clinical routine -- a strategy that might be suitable for other real applications. As demonstrated on large datasets, the proposed system can achieve, on average, 94.9%, 87.8%, and 92.5% of Cohens Kappa on helminth eggs, helminth larvae, and protozoa cysts, respectively.