diff --git a/minimum-constraints.txt b/minimum-constraints.txt
index 50ef433e..8450d945 100644
--- a/minimum-constraints.txt
+++ b/minimum-constraints.txt
@@ -64,7 +64,9 @@ requests==2.22.0; python_version >= '3.5'
 # lxml==4.2.4
 # decorator==4.0.11
 # yamlordereddictloader==0.4.0
-urllib3==1.25.9
+urllib3==1.25.9; python_version == '2.7'
+urllib3==1.24.2; python_version == '3.4'
+urllib3==1.25.9; python_version >= '3.5'
 
 # Direct dependencies for develop (must be consistent with dev-requirements.txt)
 
@@ -113,10 +115,11 @@ typed-ast==1.4.0; python_version >= '3.5' and python_version < '3.8' and impleme
 lazy-object-proxy==1.4.3
 
 # Flake8 and dependents (no imports, invoked via flake8 script):
-flake8==3.7.9
+flake8==3.8.0
 mccabe==0.6.0
-pycodestyle==2.5.0
-pyflakes==2.1.0
+pycodestyle==2.6.0a1; python_version == '3.4'
+pycodestyle==2.6.0; python_version != '3.4'
+pyflakes==2.2.0
 entrypoints==0.3.0
 functools32==3.2.3.post2; python_version == '2.7'  # technically: python_version < '3.2'
 
@@ -168,7 +171,6 @@ jsonschema==2.5.1
 jupyter_client==4.4.0
 jupyter_console==5.0.0
 jupyter_core==4.2.1
-lazy-object-proxy==1.4.2
 linecache2==1.0.0
 MarkupSafe==0.23
 mistune==0.8.1