The idle containership fleet has increased as a result of vessels having scrubbers retrofitted.
There were 118 vessels out of action on 8 July, Alphaliner said.
They account for 371,680 teu, with a "steady stream" of ships entering shipyards to have exhaust gas cleaners fitted, it added.
Alphaliner counts vessels as idle from day one if the work is being carried out separate from routine repairs.
But ships having repairs and retrofits at the same time are classed as out of action only from day 40 in the yard.
"The scrubber retrofits that involve the larger sizes generate a demand for substitute vessels that has filtered down to the classic panamax sizes," the consultancy said.
"The number of idle units of 3,000-5,100 teu has fallen to 13 units compared to over 60 units in February this year as the shortage of larger tonnage in the market have forced some operators to switch to classic panamax units as replacements."
It added that demand, particularly in the transpacific trade, in coming weeks is expected to keep units above 4,000 teu busy for the time being.
"But the summer peak season demand has so far failed to filter down to the smaller sizes with idle numbers staying stubbornly high," it said.