The move would encourage new savers not to withdraw money for at least two years - or miss a large bonus paid to long-term savers. This would deter short-term carpetbaggers from withdrawing money immediately after a windfall gain.
Yorkshire last year attempted to stop carpetbaggers disrupting its business by boosting its minimum opening balance to pounds 2,000 on share accounts - the accounts which give members a chance to vote on whether to float a society.
Smaller savers have been offered deposit accounts with no votes and no entitlement to a windfall. But from July, the Building Societies Act 1997 will bar Yorkshire from offering non-voting accounts unless customers insist on them. Unless Yorkshire drops the minimum balance, it could cut itself out of the market for small savings.
David Anderson, chief executive of the Yorkshire, said: "After July we can only offer share accounts and not the deposit accounts we have offered to smaller savers. That could mean we lose our ability to offer accounts to small savers, which is not a position we want to be in."
The scheme, which is one of several options being considered, would mean that long-term savings accounts would become the staple product of the Yorkshire.
The society, which has more than a million members, admitted the scheme would not stop members voting for conversion. But it would stop votes being distorted by temporary members who stayed only to wait for a windfall.
Other options to put off carpetbaggers include adopting a tactic used by rival building society Nationwide, where new savers have to sign away their windfall rights to charity.
Yorkshire would use the same method but would give members their windfall rights back after a set number of years.
The Yorkshire yesterday said its mortgage customers had already saved more over two years in lower rates than customers of Bristol & West received in windfall payouts. A customer with a pounds 50,000, variable rate mortgage, had saved pounds 420.92 compared with customers of the Halifax.