well, there are several horror stories on this site about visa applications, so I thought I should post about a positive experience, in the hope that it may help other travellers.
I'm a UK citizen, and will be visiting Azerbaijan with my 14-year-old son this June.
I was advised by other TA members to use Azerbaijan24 for the visa applications. Now I know TA rules about not advertising, so let me add straight away that Azerbaijan24 are not cheap, it's easy to find other agencies offering lower prices. However, though I am a budget traveller at heart, I thought it best to pay a little more to an agency which has an excellent reputation on this site.
Azerbaijan24 were superb. They answered numerous mails from me asking for different visa info., over a number of months, all within 24 hours (before I had paid any money).
When I did eventually submit the relevant documents and payment, they sent everything immediately to the Azerbaijani MFA and my son's e-visa was issued after eight days (eight actual days, not eight working days). My e-visa arrived the following day.
The whole experience was painless, and I would definitely, certainly recommend Azerbaijan24.
BTW, the current e-visa rule seems to be that they give you a visa for your chosen length of stay (seven days in our case) but they are flexible about period of use (a month, mid-June to mid-July in our case), so there is some flexibility if flights etc. are changed. Also, although we are travelling in June, they issued our e-visas now in February.