Fortunately, the website of the Brazilian consulate in Miami is much clearer and more forthcoming about what is required than was the French, the last time we did this, in 2004, and they will accept applications by mail. Unfortunately, we have to sandwich the process into a narrower time window than I would have preferred—we needed our passports until the last week of June, for the trip to France, and because the visa is only good for so long after it's issued, we couldn't do far enough in advance to be sure we'd get our passports back in time to go to France.
We amassed all the elements we could back May—passport photos, filled-out visa applications, a letter of invitation for each of us from the meeting organizers, photocopies of our driver's licenses (to prove we live in Miami's jurisdiction), etc. Then, Saturday morning, I took everything to the post office and assembled the packets—they won't accept more than one application per envelope—including the specified stamped self-addressed priority-mail envelopes for the return of our passports. On the postal clerk's advice, I opted for express mail, then found, while filling out the address labels, that I needed the Miami consulate's telephone number. Drat. I had brought the address but not the phone number. Nothing for it but to drive home again and look it up.
Back at the post office, I finished addressing all the outgoing and incoming envelopes, double-checking that each envelope included all the required information and attachments, and addressed myself once again to the clerk, to buy postage for all the incoming and outgoing envelopes, plus the U.S. postal money orders specified as the only allowable way to pay the visa application fee (Brazil charges each American applicant $100, plus $10 if you apply by mail. Other applicants pay only $25-35, but fair's fair—they say right on the website that the $100 is indirect response to the similar fee the U.S. charges Brazilian applicants.) But the post office doesn't take credit cards for money orders, and I didn't have enough cash on me. Fortunately, the clerk was willing to set all my stuff aside on her desk (if she'd given it back to me, she'd have had to remove all the metered postage she'd just stuck all over it) while I hiked the quarter-mile to the nearest ATM and back (and it would be a 96-degree day, of course).
Then, I learned, U.S. postal money orders have to filled out, like checks, so I had to step out of the line again to do that, but finally, I sealed 'em up and sent 'em off, with crossed fingers and a brief incantation for luck. If all goes well, our stamped and visa'd passports should wing their way home with several days to spare before our departure for South America.