Perhaps Flyertalk is not the most appropriate venue for this question, but I have done a search here, consulted the Indian Railways site, IndiaMike, Seat61.com, et al and cannot find what I am looking for.

For travel among these major cities: Delhi, Mumbai, Bangalore, Chennai is there absolutely no train service with private compartment and private bath (and A/C of course).

The best I can find is "AC 1" where 72 passengers share 4 bathrooms!

The luxury trains (Deccan Odyssey, Golden Chariot, etc) do not fit my needs because they are fixed itinerary sightseeing tours.

I will be traveling to/in India on business and would like to keep things as relaxed as humanly possible. This means not fighting it out at both outbound and inbound airports on local flights.

I am not looking for a lot of luxury -- I do the Madrid-Paris (Goya) overnight train on older cars, but perfectly clean with private cabin, shower and toilet, and very decent dining car.

Does nothing like this exist for India among major destinations?

Thanks!