The consultation, Changing Council Governance Arrangements, includes three proposals to change the way a community can trigger a referendum on how to change its arrangements to either a directly elected mayor or indirectly elected council leader.
One is lowering the petition threshold: the current threshold is 5% of local electors. One proposal is a straight reduction from 5% to either 4%, 3%, or just 2%.
Another is allowing online petitioning in addition to traditional paper petitions.
Online petitioning by councils is on the increase and existing identity safeguards would be required.
A third area is reducing the time between referendum votes from 10 years to four years.
Communities Secretary Hazel Blears said: "People like to know someone is in charge of their town or city because they see that the buck stops somewhere.
"Both directly elected mayors and indirectly elected council leader can provide this type of leadership and reassurance."
Any petition submitted to trigger a referendum for a change in governance will be considered by the council under the new duty on councils to respond to petitions. So even where the signature threshold has not been reached the council must respond.