diff --git a/.disabled-travis.yml b/.disabled-travis.yml
index b070a9a1151..feb2d9f8775 100644
--- a/.disabled-travis.yml
+++ b/.disabled-travis.yml
@@ -30,7 +30,7 @@ env:
     - SETUP_CMD="${PYTEST_FLAGS}"
     - BUILD_CMD="pip install -e package/ && (cd testsuite/ && python setup.py build)"
     - CONDA_MIN_DEPENDENCIES="mmtf-python biopython networkx cython matplotlib scipy griddataformats hypothesis gsd codecov"
-    - CONDA_DEPENDENCIES="${CONDA_MIN_DEPENDENCIES} seaborn>=0.7.0 clustalw=2.1 netcdf4 scikit-learn joblib>=0.12 chemfiles tqdm>=4.43.0 tidynamics>=1.0.0 rdkit>=2020.03.1 h5py==2.10.0"
+    - CONDA_DEPENDENCIES="${CONDA_MIN_DEPENDENCIES} seaborn>=0.7.0 clustalw=2.1 netcdf4 scikit-learn joblib>=0.12 chemfiles tqdm>=4.43.0 tidynamics>=1.0.0 rdkit>=2020.03.1 h5py"
     - CONDA_CHANNELS='biobuilds conda-forge'
     - CONDA_CHANNEL_PRIORITY=True
     - PIP_DEPENDENCIES="duecredit parmed"
diff --git a/.github/workflows/gh-ci.yaml b/.github/workflows/gh-ci.yaml
index a4e1507eefb..954a3852b67 100644
--- a/.github/workflows/gh-ci.yaml
+++ b/.github/workflows/gh-ci.yaml
@@ -15,7 +15,7 @@ defaults:
 
 env:
   MDA_CONDA_MIN_DEPS: "pip pytest==6.1.2 mmtf-python biopython networkx cython matplotlib-base scipy griddataformats hypothesis gsd codecov"
-  MDA_CONDA_EXTRA_DEPS: "seaborn>=0.7.0 clustalw=2.1 netcdf4 scikit-learn joblib>=0.12 chemfiles tqdm>=4.43.0 tidynamics>=1.0.0 rdkit>=2020.03.1 h5py==2.10.0"
+  MDA_CONDA_EXTRA_DEPS: "seaborn>=0.7.0 clustalw=2.1 netcdf4 scikit-learn joblib>=0.12 chemfiles tqdm>=4.43.0 tidynamics>=1.0.0 rdkit>=2020.03.1 h5py"
   MDA_PIP_MIN_DEPS: 'coveralls coverage<5 pytest-cov pytest-xdist'
   MDA_PIP_EXTRA_DEPS: 'duecredit parmed'
 
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 082c556c159..1bf963528b2 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -44,7 +44,7 @@ jobs:
   - script: python -m pip install --upgrade pip setuptools wheel
     displayName: 'Install tools'
   - script: >-
-      python -m pip install
+      python -m pip install --only-binary=h5py
       cython
       hypothesis
       matplotlib
@@ -54,11 +54,10 @@ jobs:
       pytest-xdist
       scikit-learn
       scipy
-      h5py==2.10.0
+      h5py
       tqdm
     displayName: 'Install dependencies'
   # TODO: recent rdkit is not on PyPI
-  # NOTE: h5py pinned because of gh-3019
   - script: >-
       python -m pip install
       biopython
diff --git a/maintainer/conda/environment.yml b/maintainer/conda/environment.yml
index 4d4e48d7bec..1c98dfd8441 100644
--- a/maintainer/conda/environment.yml
+++ b/maintainer/conda/environment.yml
@@ -8,7 +8,7 @@ dependencies:
   - cython
   - griddataformats
   - gsd
-  - h5py==2.10.0
+  - h5py
   - hypothesis
   - joblib>=0.12
   - matplotlib==3.2.2
@@ -31,4 +31,4 @@ dependencies:
       - duecredit
       - parmed
       - msmb_theme==1.2.0
-      - sphinx-sitemap==1.0.2
\ No newline at end of file
+      - sphinx-sitemap==1.0.2
diff --git a/package/MDAnalysis/coordinates/H5MD.py b/package/MDAnalysis/coordinates/H5MD.py
index d77a06c1a38..43500b4fc20 100644
--- a/package/MDAnalysis/coordinates/H5MD.py
+++ b/package/MDAnalysis/coordinates/H5MD.py
@@ -600,7 +600,7 @@ def _read_frame(self, frame):
             else:
                 raise NoDataError("Provide at least a position, velocity"
                                   " or force group in the h5md file.")
-        except ValueError:
+        except (ValueError, IndexError):
             raise IOError from None
 
         self._frame = frame