Question

How do I make Mew obey in FireRed/LeafGreen?

Answer 1

Get badges.

Any Pokemon that you get from another person/event that has levels way higher than any trainer you've faced so far wont listen to you at all. You can make it listen, however, by getting badges. The badge you need depends on your Pokemon's level, with higher levels needing badges that are obtained later on in-game. I don't know your mew's level, so here is a table for all the badges needed for all levels of Pokemon to obey you. (You want the Indigo League column.)

Hope I could help!

Comments

I heard that in 3rd gen, Mew and Deoxys that are obtained by non legitimate means will not obey no matter how many badges you have.

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That is true, but I'm giving his mew the benefit of the doubt.