Decoder-Side Depth Estimation (DSDE) is a system firstly enabled in the novel MPEG Immersive Video (MIV) coding standard. In DSDE, only texture components are coded, while the depth is estimated at the decoder-side. This is motivated by previous work, which has shown high coding gain and pixel rate savings in DSDE. However, the computational complexity remains a concern, as high quality depth search has a high runtime and memory requirement. In this work we extend the concept of depth estimation to depth recovery. Using this mode, the decoder-side depth information is recovered through motion compensation utilizing the displacement vectors contained in the texture bitstream. This strategy enables us to replace most of the complex depth estimation processes with a simple motion compensation step, a decision that is drawn on the encoder-side and signaled per coding unit. With only minor losses in terms of synthesis PSNR and similar perceptual quality in terms of MS-SSIM, the complexity is significantly reduced. Depending on the acceptable loss, up to 80% of the moving objects depth may be motion compensated instead of estimated by a depth estimator translating into a speed-up of a factor of 104 for inter-frames compared to the reference depth estimator.