The Care Quality Commission (CQC) said standards had improved at Mid Yorkshire Hospitals NHS Trust, which runs Pinderfields, Pontefract and Dewsbury hospitals.
But concerns remain over staffing at the organisation, where some wards had fewer than 80 per cent of the required number of nurses, the CQC's latest report said.
Last year the watchdog raised concerns that there were not enough nurses to care for patients properly when inspectors visited in May and June.
Conditions were cramped on wards where extra beds had to be opened to cope with the number of patients needing care. Patients were stuck in hospital because of delayed assessments for social care and a lack of community beds.
Mid Yorkshire was rated as "requires improvement" by the CQC.
CQC inspectors visited again on October 30 to find out what action had been taken since a warning notice was issued over safety.
The latest inspection found that staffing levels had improved and the use of extra beds had reduced, but some wards were still not meeting the required ratio of nurses to patients.
The CQC's Sandra Sutton said: "At the last inspection in May, we had identified a shortage of nursing staff. During this inspection we saw that the trust had committed to an international recruitment campaign that is expected to result in increased staffing by late 2018.
“There has been no reassessment of the trust’s rating, which remains as 'requires Improvement'. However, we will continue to work with the trust to ensure that the service continues to improve.”
Inspectors previously raised concerns over the privacy of patients in temporary beds and the distress caused by patients being moved after 10pm.
The latest CQC report, published today, said: "The use of extra capacity beds had significantly reduced since the time of our initial inspection.
"Bed moves after 10pm had also significantly reduced and were now recorded as incidents. This had resulted in a positive impact on the privacy and dignity of patients receiving care."
Mid Yorkshire chief executive Martin Barkley said: “The tangible improvements recognised by the CQC are the result of our thousands of dedicated and hardworking staff who have together driven improvements for our patients.
“The CQC rightly highlight the on-going challenges we face and the further improvement we still need to make in retaining and recruiting more staff.
“In similar ways to most other NHS organisations, the trust has experienced difficulties in recruiting registered nurses to its vacant posts, and we look forward to welcoming over 80 new healthcare assistants in the next few months."