diff --git a/pyproject.toml b/pyproject.toml
index fe6894a42..86a8f0f7e 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -56,7 +56,7 @@ dependencies = [
 default = []
 curl-cffi = [
     "curl-cffi==0.5.10; os_name=='nt' and implementation_name=='cpython'",
-    "curl-cffi>=0.5.10,!=0.6.*,<0.8; os_name!='nt' and implementation_name=='cpython'",
+    "curl-cffi>=0.5.10,!=0.6.*,<0.7.2; os_name!='nt' and implementation_name=='cpython'",
 ]
 secretstorage = [
     "cffi",
diff --git a/yt_dlp/networking/_curlcffi.py b/yt_dlp/networking/_curlcffi.py
index e8a67b734..0643348e7 100644
--- a/yt_dlp/networking/_curlcffi.py
+++ b/yt_dlp/networking/_curlcffi.py
@@ -31,9 +31,9 @@ if curl_cffi is None:
 
 curl_cffi_version = tuple(map(int, re.split(r'[^\d]+', curl_cffi.__version__)[:3]))
 
-if curl_cffi_version != (0, 5, 10) and not ((0, 7, 0) <= curl_cffi_version < (0, 8, 0)):
+if curl_cffi_version != (0, 5, 10) and not ((0, 7, 0) <= curl_cffi_version < (0, 7, 2)):
     curl_cffi._yt_dlp__version = f'{curl_cffi.__version__} (unsupported)'
-    raise ImportError('Only curl_cffi versions 0.5.10, 0.7.X are supported')
+    raise ImportError('Only curl_cffi versions 0.5.10, 0.7.0 and 0.7.1 are supported')
 
 import curl_cffi.requests
 from curl_cffi.const import CurlECode, CurlOpt