(Adds details, background on accounting change)
By Ankit Ajmera and Tim Hepher
April 10 (Reuters) - Boeing Co outsold European rival Airbus almost four to one in the first quarter and increased deliveries by a stronger-than-expected 9 percent compared with the same period last year, company data showed on Tuesday.
Both sets of numbers reflect higher demand for Boeing's best-selling 737 jetliners, with 184 commercial aircraft delivered in the three months to end-March, including 132 of the single-aisle workhorse jet.
Though it too has seen strong demand for its single-aisle A320neo, Airbus is struggling to keep up deliveries due mainly to engine issues, with deliveries down 11 percent in the first quarter, prompting it to juggle priorities.
At the same time, Boeing has seen a rebound in new orders after losing last year's race. It booked 221 net aircraft orders after cancellations in the first quarter, well ahead of the 45 bagged by Airbus during the same period.
Cowen & Co said it was raising its first-quarter earnings estimate after the delivery data. Boeing shares rose 2.9 percent, buoyed by an easing of trade tensions. Boeing also announced changes in the way it publishes the total number of aircraft already sold and waiting to be built and delivered - known as the order backlog - due to new accounting standards.
Boeing said it had trimmed 66 aircraft or one percent of the total from the published order backlog, bringing it to 5,835 jets instead of 5,901 under the previous method. That compares with 7,189 logged by rival Airbus.
Boeing did not say which aircraft or airlines had been excluded from its total.
Previously, Boeing listed individual aircraft for which it had firm contracts, together with the resulting total.
Now, the total number is adjusted to fall in line with the new revenue recognition rules but individual orders are listed as before, since Boeing still has binding contracts with buyers.
Both Boeing and Airbus regularly sell more jets than they plan to build, guessing that due to market volatility and long lead times some buyers will not be able to take delivery.
In addition, either company can have concerns about the creditworthiness or status of individual carriers.
Boeing and Airbus have often sparred about the way they tally orders, with U.S. executives frequently pointing the finger at Airbus for overstating the number of planes on order. Its current list includes several cancelled A380s, though Airbus says it holds on to deals to help enforce contract rights.
Tuesday's changes appeared to represent the first time Boeing has acknowledged some of its own orders are at risk.
Airbus had no immediate comment on whether it would also change the way it reports the number of planes on order.
But it plans with its first-quarter results this month to start publishing the value of its total backlog based on actual prices after discounts, rather than the published "list prices" which are typically said to be twice what airlines pay.
It will continue to use the official catalogue prices for individual deals, however, since the terms are confidential. (Additional reporting by Arunima Banerjee in Bengaluru; Editing by Sai Sachin Ravikumar and Adrian Croft)