Some companies could save more than $300,000 on printing, postage and staff time, Doocey said. A company in his electorate had told him it posted about 32,000 letters each year and got only 100 requests for the annual report.
Two weeks ago National MP Nuk Korako faced ridicule from the Opposition after his own member's bill was drawn.
It will remove a requirement for airports to advertise lost property in a local newspaper and instead proposes they advertise it in a more modern forum, such as on the internet.
Opposition parties say such minor changes are better dealt with by way of an "omnibus" bill which wraps up a number of non-controversial measures into one bill for expediency.
Labour said Korako's bill showed National had "lost the plot" - and reflected a tactic of stacking the ballot with inconsequential bills.
Today, Labour whip and MP Chris Hipkins tweeted in response to Doocey's bill that it would prove to be a humiliation for the backbencher.
Members' bills are the only chance Opposition and backbench MPs have to get law changes they want before Parliament.
Success is down to pure luck - bills are drawn from a ballot and some MPs never have the fortune of having theirs go before Parliament.
Some have resulted in major changes. For example, the anti-smacking legislation began as a member's bill by Sue Bradford. Act leader David Seymour's voluntary euthanasia bill is currently in the ballot.
The Companies (Annual Report Notice Requirements) Amendment Bill is the second bill Doocey has had drawn.
In May, his bill that would make people collecting donations, signatures or other support disclose whether they are being paid was withdrawn.
That was despite the bill passing its first reading in August, with support from every party in Parliament. It was partly in response to increasing reports of people intimidated into donating by aggressive sales tactics used by "chuggers" - commission-based staff.
The social services committee recommended the bill not be passed after a report from Doocey that its passage would compete with work being done by the Ministry of Business, Innovation and Employment.