diff --git a/numpy/core/tests/test_numeric.py b/numpy/core/tests/test_numeric.py
index 30d92e9d0874..2facb481e9db 100644
--- a/numpy/core/tests/test_numeric.py
+++ b/numpy/core/tests/test_numeric.py
@@ -646,7 +646,7 @@ def test_floating_exceptions(self):
                 if np.dtype(ftype).kind == 'f':
                     # Get some extreme values for the type
                     fi = np.finfo(ftype)
-                    ft_tiny = fi.tiny
+                    ft_tiny = fi.machar.tiny
                     ft_max = fi.max
                     ft_eps = fi.eps
                     underflow = 'underflow'
@@ -655,7 +655,7 @@ def test_floating_exceptions(self):
                     # 'c', complex, corresponding real dtype
                     rtype = type(ftype(0).real)
                     fi = np.finfo(rtype)
-                    ft_tiny = ftype(fi.tiny)
+                    ft_tiny = ftype(fi.machar.tiny)
                     ft_max = ftype(fi.max)
                     ft_eps = ftype(fi.eps)
                     # The complex types raise different exceptions
diff --git a/numpy/core/tests/test_scalarmath.py b/numpy/core/tests/test_scalarmath.py
index 09a734284a76..5981225c1f05 100644
--- a/numpy/core/tests/test_scalarmath.py
+++ b/numpy/core/tests/test_scalarmath.py
@@ -670,8 +670,10 @@ def _test_abs_func(self, absfunc, test_dtype):
         x = test_dtype(np.finfo(test_dtype).max)
         assert_equal(absfunc(x), x.real)
 
-        x = test_dtype(np.finfo(test_dtype).tiny)
-        assert_equal(absfunc(x), x.real)
+        with suppress_warnings() as sup:
+            sup.filter(UserWarning)
+            x = test_dtype(np.finfo(test_dtype).tiny)
+            assert_equal(absfunc(x), x.real)
 
         x = test_dtype(np.finfo(test_dtype).min)
         assert_equal(absfunc(x), -x.real)
diff --git a/numpy/core/tests/test_ufunc.py b/numpy/core/tests/test_ufunc.py
index 9e7c9b743baf..0251f21a9899 100644
--- a/numpy/core/tests/test_ufunc.py
+++ b/numpy/core/tests/test_ufunc.py
@@ -12,7 +12,7 @@
 from numpy.testing import (
     assert_, assert_equal, assert_raises, assert_array_equal,
     assert_almost_equal, assert_array_almost_equal, assert_no_warnings,
-    assert_allclose, HAS_REFCOUNT,
+    assert_allclose, HAS_REFCOUNT, suppress_warnings
     )
 from numpy.compat import pickle
 
@@ -584,10 +584,12 @@ def test_true_divide(self):
                         tgt = float(x)/float(y)
                         rtol = max(np.finfo(dtout).resolution, 1e-15)
                         # The value of tiny for double double is NaN
-                        if not np.isnan(np.finfo(dtout).tiny):
-                            atol = max(np.finfo(dtout).tiny, 3e-308)
-                        else:
-                            atol = 3e-308
+                        with suppress_warnings() as sup:
+                            sup.filter(UserWarning)
+                            if not np.isnan(np.finfo(dtout).tiny):
+                                atol = max(np.finfo(dtout).tiny, 3e-308)
+                            else:
+                                atol = 3e-308
                         # Some test values result in invalid for float16.
                         with np.errstate(invalid='ignore'):
                             res = np.true_divide(x, y, dtype=dtout)
@@ -601,10 +603,12 @@ def test_true_divide(self):
                     tgt = complex(x)/complex(y)
                     rtol = max(np.finfo(dtout).resolution, 1e-15)
                     # The value of tiny for double double is NaN
-                    if not np.isnan(np.finfo(dtout).tiny):
-                        atol = max(np.finfo(dtout).tiny, 3e-308)
-                    else:
-                        atol = 3e-308
+                    with suppress_warnings() as sup:
+                        sup.filter(UserWarning)
+                        if not np.isnan(np.finfo(dtout).tiny):
+                            atol = max(np.finfo(dtout).tiny, 3e-308)
+                        else:
+                            atol = 3e-308
                     res = np.true_divide(x, y, dtype=dtout)
                     if not np.isfinite(res):
                         continue
diff --git a/numpy/core/tests/test_umath.py b/numpy/core/tests/test_umath.py
index dc3b05f43761..35d7ecbb5438 100644
--- a/numpy/core/tests/test_umath.py
+++ b/numpy/core/tests/test_umath.py
@@ -3448,9 +3448,11 @@ def test_nextafter_0():
     for t, direction in itertools.product(np.sctypes['float'], (1, -1)):
         # The value of tiny for double double is NaN, so we need to pass the
         # assert
-        if not np.isnan(np.finfo(t).tiny):
-            tiny = np.finfo(t).tiny
-            assert_(0. < direction * np.nextafter(t(0), t(direction)) < tiny)
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning)
+            if not np.isnan(np.finfo(t).tiny):
+                tiny = np.finfo(t).tiny
+                assert_(0. < direction * np.nextafter(t(0), t(direction)) < tiny)
         assert_equal(np.nextafter(t(0), t(direction)) / t(2.1), direction * 0.0)
 
 def _test_spacing(t):