It has been said that Janet Street Porter hated No Limits and it was the first thing to go when she took over.
Yes, No Limits finished at the end of 1987 (though the Radio Times billing for the final episode suggests it would be back the following year) and DEF II began in 1988. The No Limits production team (minus Jonathan King) and Jenny Powell were behind UP2U on Saturday mornings in 1988, though, inheriting some of its features, such as referring to videos as "powerplays", whatever they were.
Bit depressed that this forum is generally too young to remember DEF II. It actually got on air really quickly, I think JSP had only joined a few months before, and so in the early months it was a bit half-arsed and inherited a load of previously commissioned stuff, the first few weeks included a terrible indie music show called FSd which JSP hated because it was just the most shameless rip-off of Network 7 imaginable. One interesting thing about the first few weeks is that they had guest continuity announcers - Susie Blake was first, in character from As Seen On TV, which didn't seem a particularly fashionable choice or that relevant for the target audience (I guess the modern equivalent would be Mrs Brown introducing Sweat The Small Stuff or something), then Ruby Wax and then the fifties announcer Peter Haigh, before they just abandoned that idea.
One problem with DEF II is the slot it was in because 6pm on Mondays and Wednesdays meant it was always likely to be interrupted for sport and other events, which it was on regular occasions to the extent that in later years it would go off completely for the summer, which isn't that good if you're trying to create a proper brand. And it more or less petered out before the end, it certainly never had an official last day, but the 6pm slot continued to include teen-orientated shows after it, the Fresh Prince and Rough Guides carried on for many years after it and then you had the likes of The Simpsons and Robot Wars and all that, until BBC3 turned up.
Along simimilar lines, in about 2005 BBC3 did Destination Three for a few months, with a team of presenters linking all the shows for three hours at around 11pm, a bit like T4 but late at night. An Andi Peters production, and it didn't do much though the likes of Rufus Hound, Anita Rani and Justin Lee Collins got some screentime out of it.