Ascribing mental states to non-human agents has been shown to increase their likeability and lead to better joint-task performance in human-robot interaction (HRI). However, it is currently unclear what physical features non-human agents need to possess in order to trigger mind attribution and whether different aspects of having a mind (e.g., feeling pain, being able to move) need different levels of human-likeness before they are readily ascribed to non-human agents. The current study addresses this issue by modeling how increasing the degree of human-like appearance (on a spectrum from mechanistic to humanoid to human) changes the likelihood by which mind is attributed towards non-human agents. We also test whether different internal states (e.g., being hungry, being alive) need different degrees of humanness before they are ascribed to non-human agents. The results suggest that the relationship between physical appearance and the degree to which mind is attributed to non-human agents is best described as a two-linear model with no change in mind attribution on the spectrum from mechanistic to humanoid robot, but a significant increase in mind attribution as soon as human features are included in the image. There seems to be a qualitative difference in the perception of mindful versus mindless agents given that increasing human-like appearance alone does not increase mind attribution until a certain threshold is reached, that is: agents need to be classified as having a mind first before the addition of more human-like features significantly increases the degree to which mind is attributed to that agent.