Thanks to a solid performance from its nonrefining operations, Sunoco (NYSE: SUN) is thus far the first of the U.S. independent refiners to report first-quarter net income on an adjusted basis. By contrast, peers Valero (NYSE: VLO) and Tesoro (NYSE: TSO) had no such luck, even though the former's retail segment posted a bang-up performance.

But before we explore the details behind this good news, let's start with the money-losing refining segment. After all, that has historically been the bread and butter of Sunoco's earnings.

Refining and supply showed a first-quarter loss from continuing operations of $42 million, versus income of $14 million in the year-ago quarter. However, that is a substantial improvement from the previous quarter, which no doubt owes to firmer market fundamentals in the past months.

Throw in losses from special items, mix it up with offsetting gains, and reported results on a companywide basis come in at a loss of $63 million, or $0.53 per share. Yikes. In the year-ago quarter, Sunoco earned $0.10 per share.

I'm not suggesting that investors whistle past these ugly figures, but the rosier adjusted results do deserve attention, if only for the fact that they highlight the relative strength in Sunoco's full portfolio of businesses.

Here, when we exclude special items (the largest charge is related to a chemicals divestment), income registers $0.14 per share. Basically, that gain owes to the $75 million chipped in by the retail, logistics, and coke operations, which is up smartly from the $61 million earned in Q1 of 2009.  

In particular, I want to call out the coke segment, whose fundamentals are tied to the steelmaking industry. Management is forecasting segment earnings of $125 million to $140 million for the year. That's below the $180 million hauled in during 2009, but the discrepancy appears to be because of planned capital spending of more than $400 million this year.

If the recent strength of metal bender AK Steel (NYSE: AKS) indicates something more sustained than a drawn-out inventory restocking, then Sunoco's coking operations are poised to fuel its own blast furnace, so to speak.

That doesn't make me positive on Sunoco shares on the whole, but for investors who are stuck in a losing position, it is cause for an unleaded moment of optimism.

Fool contributor Mike Pienciak holds no financial interest in any company mentioned in this article. The Fool has a high-octane disclosure policy.