Fully analytical models of one-dimensional acoustic devices containing planar beams (rigid elastically supported or attached at one end to a flat spring, miniaturized or not) loaded with a thin fluid layer with discontinuity in thickness have been published recently. The use of such devices as MEMS transducers with reduced-size backplate is of interest because of their geometrical simplicity, hence lower fabrication complexity and cost. The use of reduced-size backplate improves the compactness of the device (the backing reservoir is directly under the moving electrode) and enables to adjust more geometrical parameters in order to optimize the behaviour of the transducer. The above mentioned models generally suffer from slightly underestimated damping because of neglected effects of sharp edges at the entering to the fluid gap through thin slits surrounding the beam and from slightly shifted resonant frequency (when underdamped), which is related to the assumption of uniform acoustic pressure in thicker parts of the fluid gap (cavity approximation). An improved analytical model of such devices is proposed herein, where the problem of sharp edges is taken into account by an approximate manner using an added mass and where a one-dimensional analytical expression for the non-uniform acoustic pressure is used for all parts of the fluid gap. As for the previous models, the thermal and viscous boundary layer effects are taken into account in all parts of the fluid gap and the thin slits surrounding the beam. The mean displacement of the beam over the surface of the fixed electrode and the corresponding acoustic pressure sensitivity of the transducer are calculated and compared to the reference results of full 3D numerical (FEM) simulation, and the discrepancies are then discussed.