Automatic transfer of text between domains has become popular in recent times. One of its aims is to preserve the semantic content while adapting to the target domain. However, it does not explicitly maintain other attributes between the source and translated text: e.g., text length and descriptiveness. Maintaining constraints in transfer has several downstream applications, including data augmentation and debiasing. We introduce a method for such constrained unsupervised text style transfer by introducing two complementary losses to the generative adversarial network (GAN) family of models. Unlike the competing losses used in GANs, we introduce cooperative losses where the discriminator and the generator cooperate and reduce the same loss. The first is a contrastive loss and the second is a classification loss — aiming to regularize the latent space further and bring similar sentences closer together. We demonstrate that such training retains lexical, syntactic and domain-specific constraints between domains for multiple benchmark datasets, including ones where more than one attribute change. We show that the complementary cooperative losses improve text quality, according to both automated and human evaluation measures.