The eight-year-old won his first couple of starts over fences in good style before being placed in Graded company at Leopardstown and Navan.
“I think he’s a very good jumper and I don’t think I’ve had him 100% fit this year yet,” said O’Grady.
“We’d had a bad hold-up with frost before Christmas and in the race at Leopardstown he had to do the donkey work for, on paper, the best two horses around at the moment (Sizing Europe and Captain Cee Bee).
“He schooled after racing on Sunday and, in a way, I was nearly regretting I didn’t run him in the novice chase that day.
“He worked well and is going to do quite a lot of work between now and Cheltenham so I hope to have a much fitter horse come Tuesday week,” the trainer told At The Races.
But O’Grady is confident Alaivan will show his true colours in the JCB Triumph Hurdle. The former John Oxx inmate had a big reputation before making his hurdling debut at Gowran, living up to the hype with a runaway success.
He suffered a surprise reverse at the hands of fellow Triumph Hurdle contender Carlito Brigante at Leopardstown over Christmas but bounced back with an impressive display at Fairyhouse last time.
“We were disappointed at Christmas but things didn’t go right for him and we’d like to think we learnt quite a lot from the race,” O’Grady told At The Races. “As a result we were able to ride him a bit different at Fairyhouse and he was able to run like the horse we hope he is.
“I was talking to Mick Kinane (former stable jockey to Oxx) one day about his size and he said he may not have a lot of size but he does have a big engine, so hopefully one will make up for the other.
“I just hope he’s good enough to carry out the job that he’s intended for.”
Meanwhile last year’s winner Quevega features among 31 entries for the David Nicholson Mares’ Hurdle at Cheltenham on March 16.
Willie Mullins’ six-year-old turned in one of the most impressive performances of last year’s Festival when scoring by 14 lengths but has been off the track since disappointing in May.
The six-year-old is one of 11 Irish-trained entries, along with stablemates J’y Vole and Morning Supreme, and Colm Murphy’s Voler La Vedette, who is unbeaten in four starts.
The home team includes a quartet from Nicky Henderson’s stable in Carole’s Legacy, Here Comes Sally, My Petra and Stravinsky Dance.
Donald McCain won the inaugural David Nicholson Mares’ Hurdle in 2008 with the recently-retired Whiteoak and could bid for another success in the Grade Two event with Alegralil.