We observe that the probability distribution of the Brownian motion with drift −cx/(1−t) where c≠1 is singular with respect to that of the classical Brownian bridge measure on [0,1], while their Cameron\tire Martin spaces are equal set-wise if and only if c>1/2, providing also examples of exponential martingales on [0,1) not extendable to a continuous martingale on [0,1]. Other examples of generalised Brownian bridges are also studied.