diff --git a/.azure-pipelines/windows.yml b/.azure-pipelines/windows.yml
index 2d63db68e0..f825bef612 100644
--- a/.azure-pipelines/windows.yml
+++ b/.azure-pipelines/windows.yml
@@ -29,8 +29,7 @@ jobs:
       displayName: 'Update build tools'
     - script: |
         python -m pip install --find-links %EXTRA_WHEELS% %DEPENDS%
-        python -m pip install nose mock coverage codecov
-        python -m pip install pytest
+        python -m pip install nose mock coverage codecov pytest
       displayName: 'Install dependencies'
     - script: |
         python -m pip install .
@@ -41,7 +40,6 @@ jobs:
         cd for_testing
         cp ../.coveragerc .
         nosetests --with-doctest --with-coverage --cover-package nibabel nibabel
-        pytest -v ../nibabel/tests/test_affines.py ../nibabel/tests/test_volumeutils.py
       displayName: 'Nose tests'
     - script: |
         cd for_testing
diff --git a/.travis.yml b/.travis.yml
index 804e198b90..81d3589769 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -130,7 +130,6 @@ script:
           cd for_testing
           cp ../.coveragerc .
           nosetests --with-doctest --with-coverage --cover-package nibabel nibabel
-          pytest -v ../nibabel/tests/test_affines.py ../nibabel/tests/test_volumeutils.py
       else
           false
       fi
diff --git a/nibabel/arrayproxy.py b/nibabel/arrayproxy.py
index eda456c4b7..b8313e8ae4 100644
--- a/nibabel/arrayproxy.py
+++ b/nibabel/arrayproxy.py
@@ -360,10 +360,13 @@ def _get_scaled(self, dtype, slicer):
         scl_slope = np.asanyarray(self._slope)
         scl_inter = np.asanyarray(self._inter)
         use_dtype = scl_slope.dtype if dtype is None else dtype
-        slope = scl_slope.astype(use_dtype)
-        inter = scl_inter.astype(use_dtype)
+
+        if np.can_cast(scl_slope, use_dtype):
+            scl_slope = scl_slope.astype(use_dtype)
+        if np.can_cast(scl_inter, use_dtype):
+            scl_inter = scl_inter.astype(use_dtype)
         # Read array and upcast as necessary for big slopes, intercepts
-        scaled = apply_read_scaling(self._get_unscaled(slicer=slicer), slope, inter)
+        scaled = apply_read_scaling(self._get_unscaled(slicer=slicer), scl_slope, scl_inter)
         if dtype is not None:
             scaled = scaled.astype(np.promote_types(scaled.dtype, dtype), copy=False)
         return scaled
diff --git a/nibabel/tests/test_proxy_api.py b/nibabel/tests/test_proxy_api.py
index b8316d7291..1694254a0c 100644
--- a/nibabel/tests/test_proxy_api.py
+++ b/nibabel/tests/test_proxy_api.py
@@ -47,6 +47,7 @@
 from .._h5py_compat import h5py, have_h5py
 from .. import ecat
 from .. import parrec
+from ..casting import have_binary128
 
 from ..arrayproxy import ArrayProxy, is_proxy
 
@@ -54,7 +55,7 @@
 from nose.tools import (assert_true, assert_false, assert_raises,
                         assert_equal, assert_not_equal, assert_greater_equal)
 
-from numpy.testing import (assert_almost_equal, assert_array_equal)
+from numpy.testing import assert_almost_equal, assert_array_equal, assert_allclose
 
 from ..testing import data_path as DATA_PATH, assert_dt_equal
 
@@ -142,7 +143,10 @@ def validate_get_scaled(self, pmaker, params):
 
         for dtype in np.sctypes['float'] + np.sctypes['int'] + np.sctypes['uint']:
             out = prox.get_scaled(dtype=dtype)
-            assert_almost_equal(out, params['arr_out'])
+            # Half-precision is imprecise. Obviously. It's a bad idea, but don't break
+            # the test over it.
+            rtol = 1e-03 if dtype == np.float16 else 1e-05
+            assert_allclose(out, params['arr_out'].astype(out.dtype), rtol=rtol, atol=1e-08)
             assert_greater_equal(out.dtype, np.dtype(dtype))
             # Shape matches expected shape
             assert_equal(out.shape, params['shape'])
@@ -192,6 +196,7 @@ class TestAnalyzeProxyAPI(_TestProxyAPI):
     shapes = ((2,), (2, 3), (2, 3, 4), (2, 3, 4, 5))
     has_slope = False
     has_inter = False
+    data_dtypes = (np.uint8, np.int16, np.int32, np.float32, np.complex64, np.float64)
     array_order = 'F'
     # Cannot set offset for Freesurfer
     settable_offset = True
@@ -216,11 +221,12 @@ def obj_params(self):
             offsets = (self.header_class().get_data_offset(),)
         else:
             offsets = (0, 16)
-        slopes = (1., 2.) if self.has_slope else (1.,)
-        inters = (0., 10.) if self.has_inter else (0.,)
-        dtypes = (np.uint8, np.int16, np.float32)
+        # For non-integral parameters, cast to float32 value can be losslessly cast
+        # later, enabling exact checks, then back to float for consistency
+        slopes = (1., 2., float(np.float32(3.1416))) if self.has_slope else (1.,)
+        inters = (0., 10., float(np.float32(2.7183))) if self.has_inter else (0.,)
         for shape, dtype, offset, slope, inter in product(self.shapes,
-                                                          dtypes,
+                                                          self.data_dtypes,
                                                           offsets,
                                                           slopes,
                                                           inters):
@@ -262,7 +268,7 @@ def sio_func():
                 dtype=dtype,
                 dtype_out=dtype_out,
                 arr=arr.copy(),
-                arr_out=arr * slope + inter,
+                arr_out=arr.astype(dtype_out) * slope + inter,
                 shape=shape,
                 offset=offset,
                 slope=slope,
@@ -325,6 +331,10 @@ class TestSpm2AnalyzeProxyAPI(TestSpm99AnalyzeProxyAPI):
 class TestNifti1ProxyAPI(TestSpm99AnalyzeProxyAPI):
     header_class = Nifti1Header
     has_inter = True
+    data_dtypes = (np.uint8, np.int16, np.int32, np.float32, np.complex64, np.float64,
+                   np.int8, np.uint16, np.uint32, np.int64, np.uint64, np.complex128)
+    if have_binary128():
+        data_dtypes.extend(np.float128, np.complex256)
 
 
 class TestMGHAPI(TestAnalyzeProxyAPI):
@@ -334,6 +344,7 @@ class TestMGHAPI(TestAnalyzeProxyAPI):
     has_inter = False
     settable_offset = False
     data_endian = '>'
+    data_dtypes = (np.uint8, np.int16, np.int32, np.float32)
 
 
 class TestMinc1API(_TestProxyAPI):