iPhone - Wi-Fi connection delay

When I turn on Wi-Fi connection on my iPhone (1G) and connect to known Wi-Fi sources (like my Apple AirPort Extreme at home) the iPhone does not immediately connect. In the settings on the iPhone it indicates that it is connected (i.e. check mark next to the Wi-Fi source), but it is not. It usually takes several minutes for the iPhone to connect. And, sometimes I have to put the iPhone to sleep, wait a few minutes and then wake it up. Only then does the iPhone actually connect to Wi-Fi. Is there a way to make the connection more immediate?