diff --git a/utils/multires/Dockerfile b/utils/multires/Dockerfile
index be26785..16f5f6f 100644
--- a/utils/multires/Dockerfile
+++ b/utils/multires/Dockerfile
@@ -7,6 +7,12 @@ ENV DEBIAN_FRONTEND noninteractive
 RUN apt-get update && apt-get install -y --no-install-recommends \
     python3 python3-dev python3-pip python3-pil hugin-tools \
  && rm -rf /var/lib/apt/lists/*
+
+# Install build dependencies for pyshtools only if binary wheel doesn't exist
+RUN pip3 download --no-deps --only-binary :all: pyshtools==4.13.1 || \
+    (apt-get install -y --no-install-recommends \
+    gcc gfortran libfftw3-dev libopenblas-dev liblapack-dev pkg-config \
+ && rm -rf /var/lib/apt/lists/*)
 RUN pip3 install --break-system-packages pyshtools==4.13.1
 
 ADD generate.py /generate.py