Multicell joint processing can mitigate inter-cell interference and thereby increase the spectral efficiency of cellular systems. Most previous work has assumed phase-aligned (coherent) transmissions from different base stations (BSTs), which is difficult to achieve in practice. In this work, a non-coherent cooperative transmission scheme for the downlink is studied, which does not require phase alignment. We consider two adjacent cells each with a single user, and assume that the BSTs share their messages through a dedicated link. Each BST transmits a superposition of two codewords, one for each receiver. Each receiver decodes its own message, and treats the signals for the other receiver as background noise. With narrow-band transmissions the achievable rate region and maximum achievable weighted sum rate are characterized by optimizing the power allocation at each BST between its two codewords. For a wideband (multicarrier) system, a dual formulation of the optimal power allocation problem across subcarriers is presented, which admits efficient numerical solution. Results show that the proposed cooperation scheme can improve the sum rate substantially at low to moderate signal-to-noise ratios.