Method for reading information from a set of electricity meters, referred to as meters, connected by an electricity supply network to a data concentrator, referred to as a concentrator, with which said meters communicate by powerline, characterised in that the method is executed by said concentrator and comprises: obtaining information representing a set of meters classified in a plurality of classes, a first class comprising meters for which no information has been collected during the execution of said method preceding a current execution, and a plurality of second classes containing meters according to a rate of response to requests for information transmitted by said concentrator, the second classes being ordered by decreasing order of response rate; during a predefined period fixing a time allocated to the concentrator for carrying out the reading of the meters in said set, running through each class one by one by increasing order of classes, passing from a class currently being read to a new class when there no longer remain any meters to be read in the class currently being read; and, in each class: defining (417; 423) a list of a predefined number of meters in the class, each meter in the list being associated with information representing a topology of the network in a zone comprising said meter having an influence on a risk of failure of the transmissions of information by said meter, referred to as risk information, said list satisfying a predetermined condition such that at least one of the meters in the list is associated with risk information below a predetermined threshold, a request for information being transmitted to each meter following insertion thereof in said list; and, for each meter in the list, on reception of a response to a request for information concerning said meter or at the expiry of a predefined maximum response time concerning said meter, updating the list by replacing said meter in the list with another meter in the class so that the updated list satisfies the predetermined condition. obtaining information representing a set of meters classified in a plurality of classes, a first class comprising meters for which no information has been collected during the execution of said method preceding a current execution, and a plurality of second classes containing meters according to a rate of response to requests for information transmitted by said concentrator, the second classes being ordered by decreasing order of response rate; during a predefined period fixing a time allocated to the concentrator for carrying out the reading of the meters in said set, running through each class one by one by increasing order of classes, passing from a class currently being read to a new class when there no longer remain any meters to be read in the class currently being read; and, in each class: defining (417; 423) a list of a predefined number of meters in the class, each meter in the list being associated with information representing a topology of the network in a zone comprising said meter having an influence on a risk of failure of the transmissions of information by said meter, referred to as risk information, said list satisfying a predetermined condition such that at least one of the meters in the list is associated with risk information below a predetermined threshold, a request for information being transmitted to each meter following insertion thereof in said list; and, for each meter in the list, on reception of a response to a request for information concerning said meter or at the expiry of a predefined maximum response time concerning said meter, updating the list by replacing said meter in the list with another meter in the class so that the updated list satisfies the predetermined condition. defining (417; 423) a list of a predefined number of meters in the class, each meter in the list being associated with information representing a topology of the network in a zone comprising said meter having an influence on a risk of failure of the transmissions of information by said meter, referred to as risk information, said list satisfying a predetermined condition such that at least one of the meters in the list is associated with risk information below a predetermined threshold, a request for information being transmitted to each meter following insertion thereof in said list; and, for each meter in the list, on reception of a response to a request for information concerning said meter or at the expiry of a predefined maximum response time concerning said meter, updating the list by replacing said meter in the list with another meter in the class so that the updated list satisfies the predetermined condition.