A house (or any portion of a house) with a flat roof, cathedral ceiling or some other attic-less construction is difficult and will require the services of a qualified contractor.
The main problem with these roofs is the limited space for insulation and ventilation. If there is already some insulation in the joist space, trying to add more may not be beneficial. However, if you decide it is worth your while to increase insulation levels, there are a number of options. Each option involves some risk of either moisture problems or thermal bridges that can reduce the effectiveness of the insulation. A technique involving blown insulation is discussed below.
Section Renovations and repair discusses both interior and exterior retrofits, including the addition of a new roof. The existing space between the ceiling and roof can be dense-packed with cellulose or glass fibre loose-fill insulation by a contractor. Densities are typically between 56 to 72 kg/m³ (3 ½ to 4 ½ lb./cu. ft.). The contractor should calculate and confirm the density for each roof cavity.
This approach eliminates roof ventilation, so it is generally not recommended (check with local building authorities first). However, the high density of the insulation, combined with comprehensive air sealing, should reduce airflow sufficiently to avoid condensation problems.
Take extra care to make sure that air leaks into the ceiling are sealed from below. This is difficult because wiring and plumbing usually puncture the ceiling in a number of places. Moreover, the partition walls may not be completely blocked off at the top, allowing large amounts of air to flow through the interior walls into the ceiling.
Where the interior walls are completely open to the ceiling, there is no easy solution unless you are prepared to have your interior walls blown full of insulation and sealed along all trim, outlets and other penetrations.