Prompt engineering is still the primary way for users of generative text-to-image models to manipulate generated images in a targeted way. Based on treating the model as a continuous function and by passing gradients between the image space and the prompt embedding space, we propose and analyze a new method to directly manipulate the embedding of a prompt instead of the prompt text. We then derive three practical interaction tools to support users with image generation: (1) Optimization of a metric defined in the image space that measures, for example, the image style. (2) Supporting a user in creative tasks by allowing them to navigate in the image space along a selection of directions of "near" prompt embeddings. (3) Changing the embedding of the prompt to include information that a user has seen in a particular seed but has difficulty describing in the prompt. Compared to prompt engineering, user-driven prompt embedding manipulation enables a more fine-grained, targeted control that integrates a user's intentions. Our user study shows that our methods are considered less tedious and that the resulting images are often preferred.