My new company asked me to name a figure after I was offered the job verbally. I went for a relatively high figure thinking they would bargain me down but they offered me exactly what I asked for. The figure is pretty much in line with the market average (well the top end) but I've checked the company's salaries on Glassdoor and it seems like they pay well over the market average. I have a lot of years experience but my industry is relatively badly paid (apart from here it seems).
Should I go back and ask for more? Or will this risk messing things up with my new employers? I've not signed anything yet.