Upgrading your Pentium 2 to a Pentium 3
The 390E, 600E, 770X, and the 770Z uses a Pentium 2 MMC2 daughterboard, which can be swapped with a Pentium 3 MMC2 daughterboard. However, this is not a straight-swap as it involves modifications to get it working optimally.
The good news is that the memory bus speed goes from 66 MHz to 100 MHz. Although, the BGA RAM (or on-board RAM) may not be able to handle the increased bus speed. If this happens and instability occurs, you can bypass this problem by disabling the on-board RAM by setting byte 2B in the BIOS to 81.
The catch is that the BIOS produces an 'Error 127' message when booting (press ESC, then F1). This is solved by setting byte 0x20 in the BIOS to 0A, by using the integrated BIOS editor from this post.
Be careful when choosing the speed of the new MMC2 daughterboard, since there may be problems with voltages/speedstep. 500MHz is a safe choice. Processors with SpeedStep seem to work too but stay at their lowest speed unless one uses physically modifies the daughter board (see the post above).
This upgrade does not apply to the 390, 600, 770, 770E, and the 770ED, as they use a Pentium 2 MMC1 daughterboard. Such daughterboards that contain the Pentium 3 and are compatible with the MMC1 socket, does not exist.
Upgrading your A20m/A20p/A21m/A21p/A22m/A22p, T20/T21/T22's CPU
As these models use Socket 495 for CPU swaps, the CPU can be upgraded up to a Mobile Pentium 3 @ 1 GHz. It is recommended to install the most capable heatsink before doing this however, as the heat dissipation will be dramatically increased.
The CPU upgrade itself is a straight-swap, but be aware that the Mobile Pentium 3 @ 1 GHz has three known versions which differ in specifications (SL53S, SL58S, SL5TF). SL53S and SL58S are identical, but SL5TF is different as it has a slightly lower temperature tolerance. Whereas SL53S and SL58S are capable of withstanding up to 100 C or 212 F of heat, SL5TF cannot withstand the same amount of heat. Instead of 100 C or 212 F, it is only rated to withstand up to 92 C or 198 F of heat. Please consider your model's heatsink performance, if it is more than capable of keeping the core temperature below 90 C, SL5TF would be fine. If that is not the case, purchase an SL53S or SL58S.