Unfortunately, you cannot demand a custom thickness through this brand.
SleepyCat offers mattresses of heights between 15.2 and 20.3 cm (6 and 8 inches).
However, you can select a custom size for your mattresses, depending upon your requirements.
You should remember that SleepyCat does not offer any trial or refund policy for custom size mattresses.
Additionally, they might take more than 10 days to get delivered to your address.