diff --git a/CHANGELOG.md b/CHANGELOG.md
index abbb1f44a..af9444b81 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,8 @@
 
 ### Features
 
+- [#1340](https://github.com/influxdata/telegraf/issues/1340): statsd: do not log every dropped metric.
+
 ### Bugfixes
 
 - [#1330](https://github.com/influxdata/telegraf/issues/1330): Fix exec plugin panic when using single binary.
diff --git a/plugins/inputs/statsd/statsd.go b/plugins/inputs/statsd/statsd.go
index 69638af06..fb191974f 100644
--- a/plugins/inputs/statsd/statsd.go
+++ b/plugins/inputs/statsd/statsd.go
@@ -27,7 +27,8 @@ const (
 	defaultSeparator = "_"
 )
 
-var dropwarn = "ERROR: Message queue full. Discarding line [%s] " +
+var dropwarn = "ERROR: statsd message queue full. " +
+	"We have dropped %d messages so far. " +
 	"You may want to increase allowed_pending_messages in the config\n"
 
 var prevInstance *Statsd
@@ -65,6 +66,8 @@ type Statsd struct {
 
 	sync.Mutex
 	wg sync.WaitGroup
+	// drops tracks the number of dropped metrics.
+	drops int
 
 	// Channel for all incoming statsd packets
 	in   chan []byte
@@ -291,7 +294,10 @@ func (s *Statsd) udpListen() error {
 			select {
 			case s.in <- bufCopy:
 			default:
-				log.Printf(dropwarn, string(buf[:n]))
+				s.drops++
+				if s.drops == 1 || s.drops%s.AllowedPendingMessages == 0 {
+					log.Printf(dropwarn, s.drops)
+				}
 			}
 		}
 	}
diff --git a/plugins/inputs/tcp_listener/tcp_listener.go b/plugins/inputs/tcp_listener/tcp_listener.go
index a420ed759..053fc927e 100644
--- a/plugins/inputs/tcp_listener/tcp_listener.go
+++ b/plugins/inputs/tcp_listener/tcp_listener.go
@@ -29,6 +29,8 @@ type TcpListener struct {
 	// is an available bool in accept, then we are below the maximum and can
 	// accept the connection
 	accept chan bool
+	// drops tracks the number of dropped metrics.
+	drops int
 
 	// track the listener here so we can close it in Stop()
 	listener *net.TCPListener
@@ -39,7 +41,8 @@ type TcpListener struct {
 	acc    telegraf.Accumulator
 }
 
-var dropwarn = "ERROR: Message queue full. Discarding metric [%s], " +
+var dropwarn = "ERROR: tcp_listener message queue full. " +
+	"We have dropped %d messages so far. " +
 	"You may want to increase allowed_pending_messages in the config\n"
 
 const sampleConfig = `
@@ -212,7 +215,10 @@ func (t *TcpListener) handler(conn *net.TCPConn, id string) {
 			select {
 			case t.in <- bufCopy:
 			default:
-				log.Printf(dropwarn, scanner.Text())
+				t.drops++
+				if t.drops == 1 || t.drops%t.AllowedPendingMessages == 0 {
+					log.Printf(dropwarn, t.drops)
+				}
 			}
 		}
 	}
diff --git a/plugins/inputs/udp_listener/udp_listener.go b/plugins/inputs/udp_listener/udp_listener.go
index 8e2637ce7..a20a5583f 100644
--- a/plugins/inputs/udp_listener/udp_listener.go
+++ b/plugins/inputs/udp_listener/udp_listener.go
@@ -25,6 +25,8 @@ type UdpListener struct {
 
 	in   chan []byte
 	done chan struct{}
+	// drops tracks the number of dropped metrics.
+	drops int
 
 	parser parsers.Parser
 
@@ -38,7 +40,8 @@ type UdpListener struct {
 // https://en.wikipedia.org/wiki/User_Datagram_Protocol#Packet_structure
 const UDP_MAX_PACKET_SIZE int = 64 * 1024
 
-var dropwarn = "ERROR: Message queue full. Discarding line [%s] " +
+var dropwarn = "ERROR: udp_listener message queue full. " +
+	"We have dropped %d messages so far. " +
 	"You may want to increase allowed_pending_messages in the config\n"
 
 const sampleConfig = `
@@ -125,7 +128,10 @@ func (u *UdpListener) udpListen() error {
 			select {
 			case u.in <- bufCopy:
 			default:
-				log.Printf(dropwarn, string(bufCopy))
+				u.drops++
+				if u.drops == 1 || u.drops%u.AllowedPendingMessages == 0 {
+					log.Printf(dropwarn, u.drops)
+				}
 			}
 		}
 	}