Present approximate second order methods for the analysis of unbraced multistorey frames may significantly underestimate moments in single curvature regions. To clarify reasons for this that may not be well understood, the mechanics of column interaction in single curvature regions are studied. Suitable tools for sidesway description are derived, including a nearly exact, explicit free-sway effective length expression, that, when high accuracy is required, eliminates the need for cumbersome, iterative solutions of exact effective lengths from the transcendental instability equation. Two reasons for the underestimation are identified. One is related to the local second order "N-delta" effects, and the other to second order effects causing changes in rotational restraint stiffness at column ends due to vertical, inter-storey column interaction. A modified approximate storey magnifier approach is proposed that accounts for these local second order effects through two separate "flexibility factors". The approach is sufficiently simple to be viable in practical analyses, and predictions are found to compare well with more accurate results.