I think I used the word  'mega'  incorrectly when asking about
cassettes.
The cassette we have that does not work is 4cm long, 2.7cm wide and
1.2cm deep.
It has a hinged closure and smooth sides.
Our old cassette is 4.1cm long, 2.8cm wide and 1.2cm deep.
The side has a ridge to help secure the cassette in the chuck.
The interior dimensions also differ (older cassette is larger).
I've come to the conclusion that there are two types of 'deep' cassettes
on the market.
To everyone that has responed Thank you.
Carol Ann Bobrowitz