diff --git a/juju/client/connection.py b/juju/client/connection.py
index 3d680175..ff6d8ee6 100644
--- a/juju/client/connection.py
+++ b/juju/client/connection.py
@@ -17,7 +17,7 @@
 from juju import errors, tag, utils, jasyncio
 from juju.client import client
 from juju.utils import IdQueue
-from juju.version import TARGET_JUJU_VERSION
+from juju.version import CLIENT_VERSION
 
 log = logging.getLogger('juju.client.connection')
 
@@ -963,7 +963,7 @@ def _build_facades(self, facades_from_connection):
     async def login(self):
         params = {}
         # Set the client version
-        params['client-version'] = TARGET_JUJU_VERSION
+        params['client-version'] = CLIENT_VERSION
         params['auth-tag'] = self.usertag
         if self.password:
             params['credentials'] = self.password
diff --git a/juju/client/connector.py b/juju/client/connector.py
index 69840620..f1fe54a5 100644
--- a/juju/client/connector.py
+++ b/juju/client/connector.py
@@ -4,6 +4,8 @@
 import copy
 import logging
 
+from packaging import version
+
 import macaroonbakery.httpbakery as httpbakery
 
 from juju.client import client
@@ -11,8 +13,8 @@
 from juju.client.gocookies import GoCookieJar, go_to_py_cookie
 from juju.client.jujudata import API_ENDPOINTS_KEY, FileJujuData
 from juju.client.proxy.factory import proxy_from_config
-from juju.errors import JujuConnectionError, JujuError
-from juju.version import SUPPORTED_MAJOR_VERSION, TARGET_JUJU_VERSION
+from juju.errors import JujuConnectionError, JujuError, JujuUnknownVersion
+from juju.version import CLIENT_VERSION
 
 log = logging.getLogger("connector")
 
@@ -86,16 +88,20 @@ async def connect(self, **kwargs):
             self._connection = await Connection.connect(**kwargs)
 
         # Check if we support the target controller
-        juju_server_version = self._connection.info["server-version"]
-        if not juju_server_version.startswith(TARGET_JUJU_VERSION):
-            log.debug(
-                "This version was tested using {} juju version {} may have compatibility issues".format(
-                    TARGET_JUJU_VERSION, juju_server_version
-                )
-            )
-        if not self._connection.info["server-version"].startswith(
-            SUPPORTED_MAJOR_VERSION
-        ):
+        server_version = self._connection.info["server-version"]
+        try:
+            juju_server_version = version.parse(server_version)
+        except version.InvalidVersion as err:
+            # We're only interested in the major version, so
+            # we attempt to clean up versions such as 3.4-rc1.2 as just 3.4
+            if '-' not in server_version:
+                raise JujuUnknownVersion(err)
+            juju_server_version = version.parse(server_version.split('-')[0])
+
+        # CLIENT_VERSION statically comes from the VERSION file in the repo
+        client_version = version.parse(CLIENT_VERSION)
+
+        if juju_server_version.major != client_version.major:
             raise JujuConnectionError(
                 "juju server-version %s not supported" % juju_server_version
             )
diff --git a/juju/errors.py b/juju/errors.py
index b996ea7f..d0284158 100644
--- a/juju/errors.py
+++ b/juju/errors.py
@@ -137,3 +137,7 @@ class AbstractMethodError(Exception):
 
 class PylibjujuError(JujuError):
     pass
+
+
+class JujuUnknownVersion(PylibjujuError):
+    pass
diff --git a/juju/version.py b/juju/version.py
index 3035fce9..e4289b46 100644
--- a/juju/version.py
+++ b/juju/version.py
@@ -1,16 +1,19 @@
 # Copyright 2023 Canonical Ltd.
 # Licensed under the Apache V2, see LICENCE file for details.
 
+import pathlib
+import re
 
 LTS_RELEASES = ["jammy", "focal", "bionic", "xenial", "trusty", "precise"]
 
 DEFAULT_ARCHITECTURE = 'amd64'
 
-# Juju server version we target. Depending on this value, the Juju server
-# may stop the connecting considering us not compatible.
-TARGET_JUJU_VERSION = '3.2.0'
-
-# Used by connector to determine if we are compatible with the juju server
-SUPPORTED_MAJOR_VERSION = '3'
-
-SUPPORTED_MAJOR_MINOR_VERSION = '3.2'
+# CLIENT_VERSION (that's read from the VERSION file) is the highest Juju server
+# version that this client supports.
+# Note that this is a ceiling. CLIENT_VERSION <= juju-controller-version works.
+# For CLIENT_VERSION < juju-controller-version (strictly smaller), we emit a warning
+# to update the client to the latest.
+# However, for any CLIENT_VERSION > juju-controller-version, a "client incompatible
+# with server" will be returned by the juju controller.
+VERSION_FILE_PATH = pathlib.Path(__file__).parent.parent / 'VERSION'
+CLIENT_VERSION = re.search(r'\d+\.\d+\.\d+', open(VERSION_FILE_PATH).read().strip()).group()