How much in advance to book Swedish train tickets to get lowest prices?

So far I have noted two different policies on train tickets: Some companies such as DB (German railways) have a standard fare and cheaper tickets that you must book in advance, have a fixed quota per train, and if they’re gone, they’re gone and you are stuck with a more expensive ticket. Other companies such as the Belgian state railways just have a single price for a journey and there is no way of saving by optimising one’s time of booking.

I am aware that when booking trains in Sweden via SJ.se, I can choose between non-rebookable non-refundable tickets, rebookable but non-refundable ones and refundable ones. Typically, the non-rebookable ones are the cheapest by some thirty or fifty crowns.

Is it preferential to book tickets as early as possible? Are there pre-booking discounts following the German model that will be gone when they’re gone?
Or are there last-minute offers that significantly lower the price? Given the potential discomfort of having to take a different train does it sometimes make sense waiting for the last minute?
Or does it not matter, as the non-rebookable tickets will always be sold for the same price?

In case this varies by train company and depending on whether I am taking long-distance or regional trains, please consider long-distance trains preferentially and SJ trains as a second preference.