Dear all who advised me,
here is a pic of my recently acquired fretless: Warwick RockBass Streamer Standard.
I replaced the original roundwounds with LaBella flats.
The neck is rather thin compared to that of my DB, so I have to get used to that.
The instrument is rather light-weight, at 3.7 kilos.
I was able to bargain it down to 630 €, so am quite happy.