Data anonymization methods have been investigated as strategies to provide data privacy and to minimize prejudices against minorities. Recent works on machine learning have shown impressive results in generating new examples of images using Generative Adversarial Networks (GAN). Creating synthetic facial images that resembles a group, but no one in particular seem an interesting strategy to anonymize a face. Nevertheless, the image synthesis process is computationally expensive and requires a very large training dataset to produce a human-acceptable outcome. This paper presents an investigation on the trade-off between the required number of instances (size) and the images’ inter-variability of a training set for using Deep Convolutional Generative Adversarial Network (DCGAN) to generate human-acceptable synthetic images. We report an experiment using the Appen crowdsourcing platform to evaluate the human acceptance of the synthetic images generated by our DCGAN trained using different samples of the CelebA public dataset, taken according to facial attributes, such as cheekbones protuberance, face shape and eyebrow thickness. The results indicate that (1) Facial attributes have a significant effect on diminishing the images’ inter-variability, specially face shape; (2) smaller images’ inter-variability leads to smaller required training dataset and (3) filtering the DCGAN’s training datasets using oval face shape led to a required dataset almost 50% lesser than without filtering for generating images humanly acceptable. We believe this result may help individuals to anonymize their visual data maintaining certain characteristics but keeping their privacy at a lower computational cost.