The lean to conservatory is the obvious choice when fitting a conservatory where there is limited available height for the wall plate.
For instance, fitting to a bungalow with low fascias can cause problems. The minimum roof pitch for a glass roof is 10%. If the pitch is lower than this then the rain water will not run away easily. there is also the possibility that the rain water will creep back up the glass and cause possible leaks due to capillary action.
The conservatory shown here is a Double Hipped lean to, very popular and a very attractive design.