diff --git a/Makefile b/Makefile
index a876214964249b17a26b78d96f056f2ad2958952..261206180791cfbd868f814826c62596d62d1233 100644
--- a/Makefile
+++ b/Makefile
@@ -97,8 +97,8 @@ compile-requirements: ## Re-compile *.in requirements to *.txt
 	for f in $(REQ_FILES); do \
 		echo ; \
 		echo "== $$f ===============================" ; \
-		echo "pip-compile -v --no-emit-trusted-host --no-index $$REBUILD ${COMPILE_OPTS} -o $$f.txt $$f.in"; \
-		pip-compile -v --no-emit-trusted-host --no-index $$REBUILD ${COMPILE_OPTS} -o $$f.txt $$f.in || exit 1; \
+		echo "pip-compile -v --no-emit-trusted-host --no-emit-index-url $$REBUILD ${COMPILE_OPTS} -o $$f.txt $$f.in"; \
+		pip-compile -v --no-emit-trusted-host --no-emit-index-url $$REBUILD ${COMPILE_OPTS} -o $$f.txt $$f.in || exit 1; \
 		export REBUILD=''; \
 	done
 	# Post process all of the files generated above to work around open pip-tools issues
diff --git a/requirements/constraints.txt b/requirements/constraints.txt
index 6ceb9db59851e198d125dfb10170695be3029a3d..a09049ea20634d48bc5519407e8906ad9724c996 100644
--- a/requirements/constraints.txt
+++ b/requirements/constraints.txt
@@ -48,9 +48,6 @@ oauthlib==3.0.1
 # django-auth-toolkit==1.3.3 requires oauthlib>=3.1.0 which is pinned because of test failures
 django-oauth-toolkit<=1.3.2
 
-# ARCHBOM-1141: pip-tools upgrade requires pip upgrade
-pip-tools<6.0
-
 # Upgrading to 2.5.3 on 2020-01-03 triggered "'tzlocal' object has no attribute '_std_offset'" errors in production
 python-dateutil==2.4.0
 # matplotlib>=3.4.0 requires python-dateutil>=2.7
diff --git a/requirements/edx/development.txt b/requirements/edx/development.txt
index ec6c32992aaa833504131d809781ff101a98394d..d993eb0ce178e8d47c959ae646eaec6b667a2793 100644
--- a/requirements/edx/development.txt
+++ b/requirements/edx/development.txt
@@ -910,6 +910,10 @@ pbr==5.6.0
     # via
     #   -r requirements/edx/testing.txt
     #   stevedore
+pep517==0.10.0
+    # via
+    #   -r requirements/edx/pip-tools.txt
+    #   pip-tools
 piexif==1.1.3
     # via -r requirements/edx/testing.txt
 pillow==8.2.0
@@ -917,10 +921,8 @@ pillow==8.2.0
     #   -r requirements/edx/testing.txt
     #   edx-enterprise
     #   edx-organizations
-pip-tools==5.5.0
-    # via
-    #   -c requirements/edx/../constraints.txt
-    #   -r requirements/edx/pip-tools.txt
+pip-tools==6.1.0
+    # via -r requirements/edx/pip-tools.txt
 pluggy==0.13.1
     # via
     #   -r requirements/edx/testing.txt
@@ -1355,8 +1357,10 @@ tincan==1.0.0
     #   edx-event-routing-backends
 toml==0.10.2
     # via
+    #   -r requirements/edx/pip-tools.txt
     #   -r requirements/edx/testing.txt
     #   mypy
+    #   pep517
     #   pylint
     #   pytest
     #   pytest-cov
diff --git a/requirements/edx/pip-tools.txt b/requirements/edx/pip-tools.txt
index e8264f7075fa9c6b63f369ae28e788389c2b0e1f..ac0b78950041918eab22bfac73e222c0f0fd9fb8 100644
--- a/requirements/edx/pip-tools.txt
+++ b/requirements/edx/pip-tools.txt
@@ -8,10 +8,12 @@ click==7.1.2
     # via
     #   -c requirements/edx/../constraints.txt
     #   pip-tools
-pip-tools==5.5.0
-    # via
-    #   -c requirements/edx/../constraints.txt
-    #   -r requirements/edx/pip-tools.in
+pep517==0.10.0
+    # via pip-tools
+pip-tools==6.1.0
+    # via -r requirements/edx/pip-tools.in
+toml==0.10.2
+    # via pep517
 
 # The following packages are considered to be unsafe in a requirements file:
 # pip
diff --git a/requirements/pip.txt b/requirements/pip.txt
index b548e96f0cf55c1f5dc862d6272c925284e192e3..d01924638d27e843ef86405a962b45139c2806c8 100644
--- a/requirements/pip.txt
+++ b/requirements/pip.txt
@@ -1,2 +1,2 @@
-pip==20.2.3
+pip==20.3.4
 wheel==0.35.1