With first-quarter earnings largely in the rear-view mirror, the oil services analysts at Deutsche Bank A.G. (NYSE: DB) wanted to revisit the thesis for each of their top stocks to buy. In each case, they revealed what they had gleaned from the first-quarter results, recent developments since the reports and upcoming catalysts. They remain positive on the group overall, with a bias toward service and a less constructive view on non-Gulf of Mexico offshore drillers.

The underlying trends in the first quarter were very favorable, as North American margins improved sequentially, despite a decline in the rig count, suggesting significant operating leverage as activity levels recover. Going forward, U.S. drilling permits have risen strongly (onshore and in the Gulf of Mexico) and the Deutsche Bank team believes the next catalyst for the group is an increase in the rig count.

With all of these positives, Deutsche Bank has four top stocks to buy, and some other favorite names.

Baker Hughes Inc. (NYSE: BHI) has seen a large bump in revenue from the increased Gulf of Mexico drilling. The Deutsche Bank price target on the stock is $59. The Thomson/First Call estimate for the stock is much lower at $49.50. Investors receive a 1.30% dividend.

Halliburton Co. (NYSE: HAL) is another large cap stock to buy. Although the company is indemnified from the operator in its contract from the Deepwater Horizon/Macondo disaster in 2010, negative press and the possibility of an adverse settlement has kept a lid on the stock. The Deutsche Bank price target is 56. The consensus target for the stock is lower at 50. Shareholders receive a 1.10% dividend.

Nabors Industries Ltd. (NYSE: NBR) is a pure drilling play, and free cash flow, which had been negative in recent years, is expected to reach $800 million this year, and more than $1 billion in 2014, according to management guidance. Deutsche Bank has $24 price target. The consensus for the stock is considerably lower at $18. Investors are paid a 1.00% dividend.

Hercules Offshore Inc. (NASDAQ: HERO) is the small-cap stock to buy on the Deutsche Bank list. The company is enjoying a strengthening Gulf of Mexico pricing environment with leading edge jackup rates up 8% year-to-date and more than 50% versus the first four months of last year. The Deutsche Bank price target is $10, and the consensus is at $9.

Schlumberger Ltd. (NYSE: SLB) was another mega-cap giant mentioned in the report. Deutsche Bank expects it also to benefit greatly as the industry redeploys drilling rigs. The consensus price target for the stock is $91.50. Shareholders are paid a 1.60% dividend.

Weatherford International Ltd. (NYSE: WFT) hit a 52-week high last week. The company provides equipment and services used in the drilling, evaluation, completion, production and intervention of oil and natural gas wells worldwide. The consensus price target for the stock is $15.50.

The Deutsche Bank analysts continue to see the large-cap diversified service companies as best positioned over the balance of 2013. They also have noticed the U.S. land market bottoming out, led by pressure pumping and completion related services. The larger players, with their ability to bundle services and deliver the efficiencies that customers increasingly demand, seem to be taking share against this backdrop.

With the United States’ increasing role as a major oil exporter, domestic work should only increase for the top companies featured at Deutsche Bank. These top stocks to buy may be an investor’s best way to take advantage of this increase.

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