What is the best way to tame a slightly bright speaker?

I have very revealing speakers that tend to sound bright with substandard recordings. I bought a schiit loki  and it works very very well.  For $149 it’s definitely worth a try.Also you could maybe try swapping out the diaphragm for a non-metallic diaphragm.Also some people mentioned padding  down the crossovers and others cautioned against it. I would definitely try it just record the values of the stock configuration that way you can always put it back. 

It is very easy to change the balance and dynamics of the system with loading the source component. It is much like loading a MC cartridge properly.
I have the Tortuga LDR attenuator in my preamp which allows loading on the fly and I can dramatically change the overall balance and dynamics by changing the input loading while listening.lower input impedance softens treble and has an impact on dynamics. Higher impedance has more treble registers but can get wiry.
The bottom line is that you can alter the system to an optimal state for your source Zout / cables / Zin and get an optimal state. A lot of "Bright" speakers are simply faster and are better at revealing these imbalances.

this is pretty easy stuff and should really have been included in any high end component.

you can tinker the crossover.  Use paper in oil caps for the Tweeter and midrange.   Metalized poly caps are kind of bright especially when it comes to Mag and Be materials.  

Thank you again everyone.  Don't worry, I'm not going to try to replace parts in the crossover.  I'm not saying that those who suggested that are wrong, it's just that  I don't have the skills required.

I  am trying the simplest, least expensive solutions first and I'm making  progress on that front.  So I have plenty of ideas to work with.  I'll get it sorted out.

Try a master set.  This will help everything. Also, add a pair REL’s.