diff --git a/Dockerfile-core b/Dockerfile-core
index febc32a..073e5e1 100644
--- a/Dockerfile-core
+++ b/Dockerfile-core
@@ -31,7 +31,7 @@ RUN echo "setOverrideLogLevel(os.getenv('LOG_LEVEL', 'INFO'))" >/etc/ocrd_loggin
 # We use get-pip.py here to avoid
 # a. having to upgrade from Ubuntu's pip
 # b. the dreaded "old script wrapper" error message
-RUN curl -sSL https://bootstrap.pypa.io/get-pip.py -o get-pip.py && \
+RUN curl -sSL https://bootstrap.pypa.io/pip/3.6/get-pip.py -o get-pip.py && \
     python3 get-pip.py && \
     rm -f get-pip.py
 
diff --git a/Dockerfile-core-cuda10.0 b/Dockerfile-core-cuda10.0
index bd43bbe..ede7d03 100644
--- a/Dockerfile-core-cuda10.0
+++ b/Dockerfile-core-cuda10.0
@@ -31,7 +31,7 @@ RUN echo "setOverrideLogLevel(os.getenv('LOG_LEVEL', 'INFO'))" >/etc/ocrd_loggin
 # We use get-pip.py here to avoid
 # a. having to upgrade from Ubuntu's pip
 # b. the dreaded "old script wrapper" error message
-RUN curl -sSL https://bootstrap.pypa.io/get-pip.py -o get-pip.py && \
+RUN curl -sSL https://bootstrap.pypa.io/pip/3.6/get-pip.py -o get-pip.py && \
     python3 get-pip.py && \
     rm -f get-pip.py
 
diff --git a/Dockerfile-core-cuda10.1 b/Dockerfile-core-cuda10.1
index d53a8e6..96967db 100644
--- a/Dockerfile-core-cuda10.1
+++ b/Dockerfile-core-cuda10.1
@@ -31,7 +31,7 @@ RUN echo "setOverrideLogLevel(os.getenv('LOG_LEVEL', 'INFO'))" >/etc/ocrd_loggin
 # We use get-pip.py here to avoid
 # a. having to upgrade from Ubuntu's pip
 # b. the dreaded "old script wrapper" error message
-RUN curl -sSL https://bootstrap.pypa.io/get-pip.py -o get-pip.py && \
+RUN curl -sSL https://bootstrap.pypa.io/pip/3.6/get-pip.py -o get-pip.py && \
     python3 get-pip.py && \
     rm -f get-pip.py