Besides time, you can affect an etch through the strength of the current flowing through the circuit. The lower the amperage, the more delicate the etch, and the finer the details. Conversely, the higher the amperage, the stronger the etch, the courser the details.
Amperage, voltage and ohms are often described using an analogy to water flowing through a pipe; in this case amperage is like the rate at which water is flowing out of a faucet. To relate it to the quality of an etch, think of it as an airbrush. When the needle is opened only slightly, a small stream of paint is released. This lower rate of flow allows an artist to achieve much finer details than if they open the needle all the way allowing a higher rate of flow and thus a broader stream of paint to be released.