Sometimes a monster has a very cool concept but it is not the right level for your players. I'm interested in particular in leveling down monsters. I play in the heroic tier only and there are many cool higher level monsters I'd rarely have a chance to use.
With the Monster Builder (or even manually) it seems rather trivial to level down a critter. To what extent does it work in play? Can you take a monster, say, 5-6 levels down without creating something unbalanced? Do downgraded monsters tend to be too strong for their level? Or they work just fine?
Leveling a monster down a full Tier in the MB can leave a few nasty things in it. For instance, Vulnerabilities & Resistance and ongoing damage tend to ballpark around 5/Tier, so if you take 13th level monster down to 8, you might want to knock down it's Resist 15 or it's ongoing/10 a bit. Similarly, crits scale with Tier, and MB parentheticals showing crit damage are just text, they won't be modified when you level down the monster, so you'll want to re-calculate max damage on the crit, and reduce the number of additional dice by have for Paragon->Heroic.
Now, I'd also like to touch on something I like to do when leveling down monsters: shifting their secondary role to keep their total exp value the same.

It helps me feel like it's "still the same monster." Obviously, of course, it doesn't work for Solos. But if you level a Standard down 4 or 5 levels, and change it to an Elite, you'll notice MB fills in the same (or about the same) exp value. 5 more, and make it a Solo, should still be about the same exp.
If you do like that idea, you should also add some powers and maybe a trait to make it more challenging when outnumbered. A minor action attack or reaction for an Elite, an action-preservation trait or power on top of that for a Solo. A high-damage or AE Encounter can also be a nice thing to add some punch to an Elite or Solo and send the message that it's a big threat.