From my experience and this is tiny experience the withholding tax is deducted, then tax at the lowest rate in Ireland is deducted and that is the total tax you have paid. If this is the case for you then I think you are still liable for some tax. I hope someone else confirms all this!
For example if they are US shares and dividends are paid by an agent here, this might be how it works. Only 20 + 15 = 35% tax has been paid, but if you are taxed at the highest rate in Ireland you need to pay the 6%. (41 - 35)
Gross Dividend EUR 6.53
US Tax 15% 0.98
(Gross - US Tax) 5.55
Irish tax 20% 1.11
Net Dividend 4.44