If a measurement is made on one half of a bipartite system then, conditioned on the outcome, the other half achieves a new reduced state. If these reduced states defy classical explanation -- that is, if shared randomness cannot produce these reduced states for all possible measurements -- the bipartite state is said to be steerable. Classifying the steerability of states is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, 2-qubit states that have a maximally mixed marginal on the first subsystem) under projective measurements. In the current work we introduce the concept of keychain models -- a special class of local hidden state models -- which allows us to study steerability outside the set of T-states. We use keychain models to give a complete classification steering within the set of partially entangled Werner states. We also give a partial classification of steering for states that arise from applying uniform noise to pure two-qubit states.