In commonplace text-based password schemes, users typically choose passwords that are easy to recall, exhibit patterns, and are thus vulnerable to brute-force dictionary attacks. This leads us to ask whether other types of passwords (e.g., graphical) are also vulnerable to dictionary attack due to users tending to choose memorable passwords. We suggest a method to predict and model a number of such classes for systems where passwords are created solely from a user’s memory. We hypothesize that these classes define weak password subspaces suitable for an attack dictionary. For user-drawn graphical passwords, we apply this method with cognitive studies on visual recall. These cognitive studies motivate us to define a set of password complexity factors (e.g., reflective symmetry and stroke-count), which define a set of classes. To better understand the size of these classes, and thus how weak the password subspaces they define might be, we use the “Draw-A-Secret” (DAS) graphical password scheme of Jermyn et al. (1999) as an example. We analyze the size of these classes for DAS under convenient parameter choices, and show that they can be combined to define apparently popular subspaces that have bit-sizes ranging from 31 to 41 – a surprisingly small proportion of the full password space (58 bits). Our results quantitatively support suggestions that user-drawn graphical password systems employ measures such as graphical password rules or guidelines, and proactive password checking.