diff --git a/CHANGES b/CHANGES
index a10543e7c5..56cd52c92c 100644
--- a/CHANGES
+++ b/CHANGES
@@ -1,3 +1,9 @@
+6094.	[bug]		Building against (or running with) libuv versions
+			1.35.0 and 1.36.0 is now a fatal error.  The rules for
+			mixing and matching compile-time and run-time libuv
+			versions have been tightened for libuv versions between
+			1.35.0 and 1.40.0. [GL #3840]
+
 6092.	[bug]		dnssec-cds failed to cleanup properly. [GL #3831]
 
 6089.	[bug]		Source ports configured for query-source,
diff --git a/configure.ac b/configure.ac
index 84d85c1132..fefe0c4707 100644
--- a/configure.ac
+++ b/configure.ac
@@ -541,9 +541,9 @@ AC_CHECK_FUNCS([pthread_setname_np pthread_set_name_np])
 AC_CHECK_HEADERS([pthread_np.h], [], [], [#include <pthread.h>])
 
 # libuv
-AC_MSG_CHECKING([for libuv])
-PKG_CHECK_MODULES([LIBUV], [libuv >= 1.0.0], [],
-		  [AC_MSG_ERROR([libuv not found])])
+PKG_CHECK_MODULES([LIBUV], [libuv >= 1.37.0], [],
+		  [PKG_CHECK_MODULES([LIBUV], [libuv >= 1.0.0 libuv < 1.35.0], [],
+				     [AC_MSG_ERROR([libuv >= 1.0.0 (except 1.35.0 and 1.36.0) not found])])])
 
 AX_SAVE_FLAGS([libuv])
 CFLAGS="$CFLAGS $LIBUV_CFLAGS"
diff --git a/doc/arm/build.inc.rst b/doc/arm/build.inc.rst
index 5bad09e2af..ccd0d32bf1 100644
--- a/doc/arm/build.inc.rst
+++ b/doc/arm/build.inc.rst
@@ -60,10 +60,12 @@ To build BIND 9, the following packages must be installed:
 - ``perl``
 - ``pkg-config`` / ``pkgconfig`` / ``pkgconf``
 
-BIND 9.18 requires ``libuv`` 1.x or higher. On older systems, an updated
-``libuv`` package needs to be installed from sources such as EPEL, PPA,
-or other native sources. The other option is to build and install
-``libuv`` from source.
+BIND 9.18 requires ``libuv`` 1.0.0 or higher, using ``libuv`` >= 1.40.0
+is recommended. Compiling or running with ``libuv`` 1.35.0 or 1.36.0 is
+not supported, as this could lead to an assertion failure in the UDP
+receive code. On older systems, an updated ``libuv`` package needs to be
+installed from sources such as EPEL, PPA, or other native sources. The
+other option is to build and install ``libuv`` from source.
 
 OpenSSL 1.0.2e or newer is required. If the OpenSSL library is installed
 in a nonstandard location, specify the prefix using
diff --git a/doc/notes/notes-current.rst b/doc/notes/notes-current.rst
index f9614f0c9c..ee329b24cf 100644
--- a/doc/notes/notes-current.rst
+++ b/doc/notes/notes-current.rst
@@ -30,7 +30,26 @@ Removed Features
 Feature Changes
 ~~~~~~~~~~~~~~~
 
-- None.
+- libuv support for receiving multiple UDP messages in a single system
+  call (``recvmmsg()``) has been tweaked several times between libuv
+  versions 1.35.0 and 1.40.0; the recommended libuv version is 1.40.0 or
+  higher. New rules are now in effect for running with a different
+  version of libuv than the one used at compilation time. These rules
+  may trigger a fatal error at startup:
+
+  - Building against or running with libuv versions 1.35.0 and 1.36.0 is
+    now a fatal error.
+
+  - Running with libuv version higher than 1.34.2 is now a fatal error
+    when :iscman:`named` is built against libuv version 1.34.2 or lower.
+
+  - Running with libuv version higher than 1.39.0 is now a fatal error
+    when :iscman:`named` is built against libuv version 1.37.0, 1.38.0,
+    1.38.1, or 1.39.0.
+
+  This prevents the use of libuv versions that may trigger an assertion
+  failure when receiving multiple UDP messages in a single system call.
+  :gl:`#3840`
 
 Bug Fixes
 ~~~~~~~~~
diff --git a/lib/isc/netmgr/netmgr.c b/lib/isc/netmgr/netmgr.c
index 01d5f168a8..ee96138721 100644
--- a/lib/isc/netmgr/netmgr.c
+++ b/lib/isc/netmgr/netmgr.c
@@ -204,10 +204,10 @@ isc__nm_threadpool_initialize(uint32_t workers) {
 #elif HAVE_DECL_UV_UDP_MMSG_FREE
 #define MINIMAL_UV_VERSION UV_VERSION(1, 40, 0)
 #elif HAVE_DECL_UV_UDP_RECVMMSG
+#define MAXIMAL_UV_VERSION UV_VERSION(1, 39, 99)
 #define MINIMAL_UV_VERSION UV_VERSION(1, 37, 0)
-#elif HAVE_DECL_UV_UDP_MMSG_CHUNK
-#define MINIMAL_UV_VERSION UV_VERSION(1, 35, 0)
 #else
+#define MAXIMAL_UV_VERSION UV_VERSION(1, 34, 99)
 #define MINIMAL_UV_VERSION UV_VERSION(1, 0, 0)
 #endif
 
@@ -218,10 +218,19 @@ isc__netmgr_create(isc_mem_t *mctx, uint32_t workers, isc_nm_t **netmgrp) {
 
 	REQUIRE(workers > 0);
 
+#ifdef MAXIMAL_UV_VERSION
+	if (uv_version() > MAXIMAL_UV_VERSION) {
+		FATAL_ERROR("libuv version too new: running with libuv %s "
+			    "when compiled with libuv %s will lead to "
+			    "libuv failures",
+			    uv_version_string(), UV_VERSION_STRING);
+	}
+#endif /* MAXIMAL_UV_VERSION */
+
 	if (uv_version() < MINIMAL_UV_VERSION) {
 		FATAL_ERROR("libuv version too old: running with libuv %s "
 			    "when compiled with libuv %s will lead to "
-			    "libuv failures because of unknown flags",
+			    "libuv failures",
 			    uv_version_string(), UV_VERSION_STRING);
 	}