The Tesla Model S P85D electric car is arguably the world's quickest production sedan, but it now seems to have another speedy distinction.

That's because the most expensive version of the Model S also has the shortest time between online order and vehicle delivery of any Tesla currently on sale.

DON'T MISS: 2014 Tesla Model S P85D: First Drive Of All-Electric AWD Performance Sedan

The average wait time for a P85D is now just 20 days, which is apparently much shorter than for any other Model S variant.

That the wait is shortest for the priciest Model S indicates Tesla is boosting production of that version to increase profits, reports The Wall Street Journal (subscription required).

Tesla's website claims that orders of the roughly $105,000 P85D will be delivered late this month, while buyers who order the $80,000 S85 or $70,000 S60 will have to wait until May to receive their cars.

The company told The Wall Street Journal that it is prioritizing deliveries of the P85D. Since Tesla doesn't release monthly sales figures, it's difficult to tell what proportion of overall sales that model accounts for, though.

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What's clear is that more sales of the more expensive P85D translate to higher profits per transaction.

That may mollify Tesla investors as the company continues to ramp up capital expenditures on projects like its Nevada battery "Gigafactory," final validation work on the Model X crossover, and early development work for its planned less-expensive Model 3 sedan.

The Journal also reports that Tesla may be building up an inventory of unsold cars--which could indicate a change in its sales model.

Tesla Model S P85D, 2015 Detroit Auto Show

Tesla Model S P85D, 2015 Detroit Auto Show

Tesla has typically built cars to order, with buyers ordering online or through company-owned retail stores rather than picking an existing vehicle on the lot of a traditional dealership.

Now, though, analysts suggest that Tesla is keeping more unsold cars around.

Credit Suisse estimated the company had 1,000 unsold units at the end of 2014, while CVC Research estimated the number was 3,000.

MORE: Why I Had To Trade My Tesla Model S For A Brand-New P85D

In a recent regulatory filing, Tesla changed its definition of "finished goods" to include cars available for immediate sale, rather than solely cars in transit to customers.

Tesla's build-to-order sales model seems unlikely to change substantially, at least in the near term, but it appears that the company may now be expanding its number of vehicles available for immediate sale--and prioritizing its most profitable versions.

For now, in other words, the customers who want their cars most quickly will need to order the quickest cars.

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