Budding viruses face a trade-off: Virions need to efficiently attach to and enter uninfected cells. At the same time, newly generated virions need to efficiently bud and detach from infected cells. This suggests that the virus needs to find a balance with regard to its ability to stick to a target cell, i.e. there should be an optimal level of stickiness. We investigate this issue using influenza A as an example. We show that an optimal level of stickiness does exist, and show how it changes in the presence of the immune response. We also show how the optimal values for detachment and attachment depend on other properties of the virus and host, such as virion production rate and target-cell death rate.