If your monitor wakes up (almost) immediately after sleep
If Firefox or other browser or any other application is not your problem, perhaps you’ll have to remove the keyboard wake up ability, keeping only the mouse as a device that would wake your PC up. In case your keyboard is not the problem, you should do the opposite, disable the mouse power up options and keep the keyboard enabled.
If keyboard or mouse did not cause the wake problem, check your “Power options” in the Control Panel, select the plan that you use (e.g. the Balanced power plan) and then click -> Change the plan settings -> Change advanced power plan settings. From the next dialog “Power options” expand the branch “Sleep”, then expand “Allow wake timers,” and choose Disable.
You may also need to open the Device Manager and disable Windows’ ability to wake on input from your Network adapter. Go also to the “Advanced” section of your Network adapter and turn to “disabled” these options: “Shutdown Wake-On-Lan”, “Wake on Magic Packet” and “Wake on pattern match.”
Check also your BIOS power settings, e.g. if there is enabled a Wake on Display Activity function (usually in Asus cards), in which case the monitor itself is waking the computer up. You may need also to check the CMOS battery, when all other solutions fail. If the battery is weak is known to cause such problems.
Of course, you don’t have to mess even with the jumper settings of your motherboard, if you can get this Super Sleep freeware to protect the sleep of your monitor.