A computer-implemented method for use in an Ethernet Virtual Private Network "EVPN", the EVPN comprising a customer site including at least one MAC-addressable device, wherein the customer site is multihomed via a customer edge device "CE" to at least two provider edge devices "PEs" (330a and 330b), the computer-implemented method for controlling advertisements of an auto-discovery per EVPN instance "A-D/EVI" route or an auto-discovery per Ethernet segment identifier "A-D/ESI" route to a remote provider edge device, wherein the remote provider edge device belongs to the EVPN but is not directly connected with the CE, the computer-implemented method comprising: a) determining, by one of the at least two provider edge devices, whether or not a MAC-learning condition is met, wherein the MAC-learning condition is at least one of: that the one of the at least two provider edge devices has received all MAC advertisements from any other PEs belonging to the EVPN and directly connected to the same multihomed site; that a predetermined time has elapsed since a link to the multihomed site has come up, and wherein the predetermined time has been selected to be sufficient for local MAC address learning; that a border gateway protocol "BGP" end of route information base "RIB" "EOR" message has been received from any other multihomed provider edge devices directly connected with the multihomed site and belonging to the EVPN; and that the one of the at least two provider edge devices has ensured that all MAC routes for the multihomed site have been programmed in its MAC table; and b) responsive to a determination that the MAC-learning condition is met, - advertising, by the one of the at least two provider edge devices, an A-D/EVI route or an A-D/ESI route to the remote provider edge device, and otherwise, responsive to a determination that the MAC-learning condition is not met, - suppressing, by the one of the at least two provider edge devices, an A-D/EVI route advertisement or an A-D/ESI route advertisement, whereby the probability of one of the at least two provider edge devices dropping or flooding packets designed for a MAC addressable device of the multihomed site is reduced. a) determining, by one of the at least two provider edge devices, whether or not a MAC-learning condition is met, wherein the MAC-learning condition is at least one of: that the one of the at least two provider edge devices has received all MAC advertisements from any other PEs belonging to the EVPN and directly connected to the same multihomed site; that a predetermined time has elapsed since a link to the multihomed site has come up, and wherein the predetermined time has been selected to be sufficient for local MAC address learning; that a border gateway protocol "BGP" end of route information base "RIB" "EOR" message has been received from any other multihomed provider edge devices directly connected with the multihomed site and belonging to the EVPN; and that the one of the at least two provider edge devices has ensured that all MAC routes for the multihomed site have been programmed in its MAC table; and b) responsive to a determination that the MAC-learning condition is met, - advertising, by the one of the at least two provider edge devices, an A-D/EVI route or an A-D/ESI route to the remote provider edge device, and otherwise, responsive to a determination that the MAC-learning condition is not met, - suppressing, by the one of the at least two provider edge devices, an A-D/EVI route advertisement or an A-D/ESI route advertisement, whereby the probability of one of the at least two provider edge devices dropping or flooding packets designed for a MAC addressable device of the multihomed site is reduced. - advertising, by the one of the at least two provider edge devices, an A-D/EVI route or an A-D/ESI route to the remote provider edge device, and otherwise, responsive to a determination that the MAC-learning condition is not met, - suppressing, by the one of the at least two provider edge devices, an A-D/EVI route advertisement or an A-D/ESI route advertisement, whereby the probability of one of the at least two provider edge devices dropping or flooding packets designed for a MAC addressable device of the multihomed site is reduced.