diff --git a/doc/src/sgml/libpq.sgml b/doc/src/sgml/libpq.sgml
index c24a69f00cc..80e55f5f382 100644
--- a/doc/src/sgml/libpq.sgml
+++ b/doc/src/sgml/libpq.sgml
@@ -1110,10 +1110,11 @@ postgresql://%2Fvar%2Flib%2Fpostgresql/dbname
       <term><literal>connect_timeout</literal></term>
       <listitem>
       <para>
-       Maximum wait for connection, in seconds (write as a decimal integer
-       string). Zero or not specified means wait indefinitely.  It is not
-       recommended to use a timeout of less than 2 seconds.
-       This timeout applies separately to each connection attempt.
+       Maximum wait for connection, in seconds (write as a decimal integer,
+       e.g. <literal>10</literal>).  Zero, negative, or not specified means
+       wait indefinitely.  The minimum allowed timeout is 2 seconds, therefore
+       a value of <literal>1</literal> is interpreted as <literal>2</literal>.
+       This timeout applies separately to each host name or IP address.
        For example, if you specify two hosts and <literal>connect_timeout</literal>
        is 5, each host will time out if no connection is made within 5
        seconds, so the total time spent waiting for a connection might be
diff --git a/src/interfaces/libpq/fe-connect.c b/src/interfaces/libpq/fe-connect.c
index 986f74ff006..9315a27561f 100644
--- a/src/interfaces/libpq/fe-connect.c
+++ b/src/interfaces/libpq/fe-connect.c
@@ -1905,6 +1905,8 @@ connectDBComplete(PGconn *conn)
 	PostgresPollingStatusType flag = PGRES_POLLING_WRITING;
 	time_t		finish_time = ((time_t) -1);
 	int			timeout = 0;
+	int			last_whichhost = -2;	/* certainly different from whichhost */
+	struct addrinfo *last_addr_cur = NULL;
 
 	if (conn == NULL || conn->status == CONNECTION_BAD)
 		return 0;
@@ -1918,12 +1920,12 @@ connectDBComplete(PGconn *conn)
 		if (timeout > 0)
 		{
 			/*
-			 * Rounding could cause connection to fail; need at least 2 secs
+			 * Rounding could cause connection to fail unexpectedly quickly;
+			 * to prevent possibly waiting hardly-at-all, insist on at least
+			 * two seconds.
 			 */
 			if (timeout < 2)
 				timeout = 2;
-			/* calculate the finish time based on start + timeout */
-			finish_time = time(NULL) + timeout;
 		}
 	}
 
@@ -1931,6 +1933,21 @@ connectDBComplete(PGconn *conn)
 	{
 		int			ret = 0;
 
+		/*
+		 * (Re)start the connect_timeout timer if it's active and we are
+		 * considering a different host than we were last time through.  If
+		 * we've already succeeded, though, needn't recalculate.
+		 */
+		if (flag != PGRES_POLLING_OK &&
+			timeout > 0 &&
+			(conn->whichhost != last_whichhost ||
+			 conn->addr_cur != last_addr_cur))
+		{
+			finish_time = time(NULL) + timeout;
+			last_whichhost = conn->whichhost;
+			last_addr_cur = conn->addr_cur;
+		}
+
 		/*
 		 * Wait, if necessary.  Note that the initial state (just after
 		 * PQconnectStart) is to wait for the socket to select for writing.
@@ -1975,18 +1992,10 @@ connectDBComplete(PGconn *conn)
 		if (ret == 1)			/* connect_timeout elapsed */
 		{
 			/*
-			 * Attempt connection to the next host, ignoring any remaining
-			 * addresses for the current host.
+			 * Give up on current server/address, try the next one.
 			 */
-			conn->try_next_addr = false;
-			conn->try_next_host = true;
+			conn->try_next_addr = true;
 			conn->status = CONNECTION_NEEDED;
-
-			/*
-			 * Restart the connect_timeout timer for the new host.
-			 */
-			if (timeout > 0)
-				finish_time = time(NULL) + timeout;
 		}
 
 		/*