Greater Anglia was one of the most improved rail companies in Britain for punctuality and reliability over the first three months of the current financial year according to the government’s Office of Road and Rail.
But only two-thirds of its train stops were "on time" (early or within a minute of the scheduled time) - although that was above the national average.
The number of trains on time increased by 3.4% to 66.6% - and the number of minutes lost to delays during the quarter fell by 10.7% during the first quarter (April to June) compared with the first three months of 2018/19. Nationally 64.7% of trains arrived on time.
The number of cancelled services fell very slightly, from 2.5% of services to 2.4%.
Greater Anglia was fifth in the national league table for improved punctuality - but the three most improved firms were services where there had been major problems last year, Govia Thameslink, Great Western, and Merseyrail.
Jamie Burles, Greater Anglia's managing director, said: "Whichever way we measure it, the main thing for us is that we want to make sure that more customers arrive at their destination on time, or even early.
"All this year we've been working with Network Rail on an "Every Second Counts" campaign to improve the performance of the railway in East Anglia so that more of our customers arrive at their destinations on time or early.
"I'm please to see that our hard work is paying off, but we will not be complacent, there is still much we can do to further improve punctuality for our customers."
As part of the Every Second Counts campaign, Greater Anglia and Network Rail hold regular "performance summits" to look at problems causing delays and analyse how to overcome them.
These improvements came before the first of the new Stadler trains was introduced on services.
A spokeswoman for Greater Anglia said the punctuality figures should improve further as more new trains are introduced because they are able to travel faster than the existing diesels.
Each new train has to run 2,000 miles across the region before it can enter passenger service. There had been no technical problems with those that had come into service - but it is a process that will take several months to complete.
Every line has to be passed for the new trains to run. The lines from Norwich to Cambridge, Lowestoft and Great Yarmouth have been cleared and some new trains are running on them. Testing is under way from Ipswich to Cambridge and Peterborough and is about to start on the Sheringham line.
Minor changes are needed to some places on the East Suffolk Line between Lowestoft and Ipswich - including Woodbridge Station - before testing can start, but they are expected to be completed during the autumn.
The locomotive-hauled services from Norwich to Lowestoft and Great Yarmouth are due to finish this weekend when the diesel engines and carriages are due to be returned to their owner Direct Rail Services (DRS).
However it is not likely to be the last time the diesel locomotives, dating from the 1960s, are seen in the region - they are likely to be hauling track-clearing trains to keep lines clear during the leaf-fall season in the autumn.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here