The following example will put the relevant computer to sleep immediately:

I closed my eyes once more, unable to resist any longer, and sleep immediately overwhelmed me.

However, despite the physical and emotional exhaustion of that wearing day, I wasn't able to sleep immediately.

Ramp may be used to temporarily lower the pressure if the user does not immediately sleep.

After getting his number, she calls the guy and immediately sleeps with him.

He and the rest slept immediately, too fatigued to eat or sleep.

Soon afterwards I had gone to bed and slept immediately.

Unable to get back to sleep immediately, she found herself thinking of the gulls as her allies.

By now he and the others were too wide awake to go back to sleep immediately.

As usual, though, when things were bothering him he couldn't get to sleep immediately.