What order for sauna, steam and spa bath?

The sauna, steam room and spa bath (aka jacuzzi). All key parts of any decent health suite. But in what order? Does it matter?

There's a lovely line in the Wikipedia entry about saunas that says:

In the United Kingdom, where public saunas are becoming increasingly fashionable, the practice of alternating between the sauna and the jacuzzi in short seatings (considered a faux pas in Northern Europe) has emerged.

Brits are Doing It Wrong! Not least because "cold showers are shunned by most", missing out the hot/cold cycle.

In practice, it depends on which facilities are busiest at any given time. But all else being equal, my routine is either:
Steam, cold shower, whirlpool, cold shower, sauna, cold shower, warm shower
or
Steam, cold shower, whirlpool, cold shower, sauna, cold shower, sauna, cold shower, warm shower, whirlpool, warm shower.

Pausing for a drink and a sit down as appropriate.

That's when I'm not simply alternating between sauna and shower.

Is there a reason for this? Well, for me I always take my cossie off before a sauna, but I don't mind wearing one in a steam room. It makes sense to put the with-cossie sections together.

What do you think?