Neural image compression has made a great deal of progress. State-of-the-art models are based on variational autoencoders and are outperforming classical models. Neural compression models learn to encode an image into a quantized latent representation that can be efficiently sent to the decoder, which decodes the quantized latent into a reconstructed image. While these models have proven successful in practice, they lead to sub-optimal results due to imperfect optimization and limitations in the encoder and decoder capacity. Recent work shows how to use stochastic Gumbel annealing (SGA) to refine the latents of pre-trained neural image compression models. We extend this idea by introducing SGA+, which contains three different methods that build upon SGA. Further, we give a detailed analysis of our proposed methods, show how they improve performance, and show that they are less sensitive to hyperparameter choices. Besides, we show how each method can be extended to three- instead of two-class rounding. Finally, we show how refinement of the latents with our best-performing method improves the compression performance on the Tecnick dataset and how it can be deployed to partly move along the rate-distortion curve.