In 1643, the Oxford Army was issued with coats, breeches and montero caps:
"all the common soldiers then at Oxford were new appareled, some all in red, coats, breeches and mounteers; & some all in blewe"Sadly no one really knows what a montero actually looked like, the Oxford English Dictionary says:
"A cap of a type formerly worn in Spain for hunting, having a spherical crown and (freq. fur lined) flaps able to be drawn down to protect the ears and neck"
In this image, Colonel Thomas Lunsford is wearing a cap with a peak and a low rounded front, very much the classic reenactor's montero. Notice how thin the band is that goes around the cap.
The next two images are very similar, one after Bosse is a French engraving and the second from Farndon Church window in Cheshire of drummers wearing the same kind of cap, this time with a band that comes to a point, and either braid or piped seams as decoration, topped off with the ubiquitous feathers.
The last two are also similar, one is a Hollar engraving, the other by Abraham Bosse, entitled Envy, both show a peakless cap with piped seams or maybe braided decoration to the crown, which is made of more panels this time, maybe 12 or so and a folded band that comes to a point in front like the drummer's one. The right hand image also shows the folding of the band though I suspect, having made a few, that the artist doesn't quite understand how they work. The detail does show though that the band is butt stitched together at the front. Both have a button on the top that covers the tricky part of the crown where the seams meet.
This second example is made more to the Lunsford pattern with a rounded front to the band
And now a third example, my best take on the peakless Envy montero.