diff --git a/pandas/core/construction.py b/pandas/core/construction.py
index 78a7f1890b5de..db2a4c40e7536 100644
--- a/pandas/core/construction.py
+++ b/pandas/core/construction.py
@@ -498,6 +498,9 @@ def sanitize_array(
         if dtype is not None and is_float_dtype(data.dtype) and is_integer_dtype(dtype):
             # possibility of nan -> garbage
             try:
+                # Note: we could use try_cast_integer_dtype
+                #  (or even maybe_cast_to_integer_array) but
+                #  we can get non-numpy integer-dtypes here
                 subarr = _try_cast(data, dtype, copy, True)
             except ValueError:
                 subarr = np.array(data, copy=copy)
@@ -633,6 +636,38 @@ def _maybe_repeat(arr: ArrayLike, index: Optional[Index]) -> ArrayLike:
     return arr
 
 
+def try_cast_integer_dtype(
+    arr: Union[list, np.ndarray], dtype: np.dtype, copy: bool, raise_cast_failure: bool
+) -> np.ndarray:
+    # Caller is responsible for checking
+    #  - is_integer_dtype(dtype)
+
+    # GH#15832: Check if we are requesting a numeric dtype and
+    #  that we can convert the data to the requested dtype.
+    try:
+        # this will raise if we have e.g. floats
+        return maybe_cast_to_integer_array(arr, dtype, copy=copy)
+    except OverflowError:
+        if not raise_cast_failure:
+            # i.e. reached from DataFrame constructor; ignore dtype
+            #  and cast without silent overflow
+            return np.array(arr, copy=copy)
+        raise
+    except ValueError as err:
+        if "Trying to coerce float values to integers" in str(err):
+            if not raise_cast_failure:
+                # Just do it anyway, i.e. DataFrame(floats, dtype="int64")
+                #  is equivalent to DataFrame(floats).astype("int64")
+
+                # error: Argument 1 to "construct_1d_ndarray_preserving_na"
+                # has incompatible type "Union[List[Any], ndarray]";
+                # expected "Sequence[Any]"
+                return construct_1d_ndarray_preserving_na(
+                    arr, dtype, copy=copy  # type: ignore[arg-type]
+                )
+        raise
+
+
 def _try_cast(
     arr: Union[list, np.ndarray],
     dtype: Optional[DtypeObj],
@@ -682,14 +717,8 @@ def _try_cast(
         # GH#15832: Check if we are requesting a numeric dtype and
         # that we can convert the data to the requested dtype.
         if is_integer_dtype(dtype):
-            # this will raise if we have e.g. floats
-
-            # error: Argument 2 to "maybe_cast_to_integer_array" has incompatible type
-            # "Union[dtype, ExtensionDtype, None]"; expected "Union[ExtensionDtype, str,
-            # dtype, Type[str], Type[float], Type[int], Type[complex], Type[bool],
-            # Type[object]]"
-            maybe_cast_to_integer_array(arr, dtype)  # type: ignore[arg-type]
-            subarr = arr
+            dtype = cast(np.dtype, dtype)
+            return try_cast_integer_dtype(arr, dtype, copy, raise_cast_failure)
         else:
             subarr = maybe_cast_to_datetime(arr, dtype)
             if dtype is not None and dtype.kind == "M":
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 44650500e0f65..6683a08b84622 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -2140,6 +2140,13 @@ def maybe_cast_to_integer_array(
     if is_float_dtype(arr) or is_object_dtype(arr):
         raise ValueError("Trying to coerce float values to integers")
 
+    if casted.dtype < arr.dtype:
+        # e.g. orig=[1, 200, 923442] and dtype='int8'
+        raise OverflowError(f"Trying to coerce too-large values to {dtype}")
+
+    # Not sure if this can be reached, but covering our bases
+    raise ValueError(f"values cannot be losslessly cast to {dtype}")
+
 
 def convert_scalar_for_putitemlike(scalar: Scalar, dtype: np.dtype) -> Scalar:
     """
diff --git a/pandas/core/internals/construction.py b/pandas/core/internals/construction.py
index 63a437a91f6e4..fd45955fc7c66 100644
--- a/pandas/core/internals/construction.py
+++ b/pandas/core/internals/construction.py
@@ -45,6 +45,7 @@
     is_named_tuple,
     is_object_dtype,
 )
+from pandas.core.dtypes.dtypes import ExtensionDtype
 from pandas.core.dtypes.generic import (
     ABCDataFrame,
     ABCDatetimeIndex,
@@ -64,6 +65,7 @@
 from pandas.core.construction import (
     extract_array,
     sanitize_array,
+    try_cast_integer_dtype,
 )
 from pandas.core.indexes import base as ibase
 from pandas.core.indexes.api import (
@@ -249,7 +251,7 @@ def ndarray_to_mgr(
         if not len(values) and columns is not None and len(columns):
             values = np.empty((0, 1), dtype=object)
 
-    if is_extension_array_dtype(values) or is_extension_array_dtype(dtype):
+    if is_extension_array_dtype(values) or isinstance(dtype, ExtensionDtype):
         # GH#19157
 
         if isinstance(values, np.ndarray) and values.ndim > 1:
@@ -266,20 +268,27 @@ def ndarray_to_mgr(
 
     # by definition an array here
     # the dtypes will be coerced to a single dtype
+    # TODO: the was_masked check is to avoid breaking a very sketchy-looking
+    #  test_constructor_maskedarray
+    was_masked = isinstance(values, np.ma.MaskedArray)
     values = _prep_ndarray(values, copy=copy)
-
     if dtype is not None and not is_dtype_equal(values.dtype, dtype):
         shape = values.shape
         flat = values.ravel()
 
-        if not is_integer_dtype(dtype):
-            # TODO: skipping integer_dtype is needed to keep the tests passing,
-            #  not clear it is correct
+        to_int = is_integer_dtype(dtype)
+        if not was_masked and to_int:
+            values = try_cast_integer_dtype(
+                flat, dtype=dtype, copy=copy, raise_cast_failure=False
+            )
+        elif not to_int:
             # Note: we really only need _try_cast, but keeping to exposed funcs
             values = sanitize_array(
                 flat, None, dtype=dtype, copy=copy, raise_cast_failure=True
             )
         else:
+            # TODO: we get here with test_constructor_maskedarray_nonfloat2
+            #  which looks like the test may be wrong
             try:
                 values = construct_1d_ndarray_preserving_na(
                     flat, dtype=dtype, copy=False
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index 285d6286931af..993f6c2cf5fe9 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -17,7 +17,10 @@
 import pytest
 import pytz
 
-from pandas.compat import np_version_under1p19
+from pandas.compat import (
+    is_platform_windows,
+    np_version_under1p19,
+)
 import pandas.util._test_decorators as td
 
 from pandas.core.dtypes.common import is_integer_dtype
@@ -338,6 +341,23 @@ def test_constructor_int_overflow(self, values):
         assert result[0].dtype == object
         assert result[0][0] == value
 
+    @pytest.mark.xfail(
+        is_platform_windows(), reason="dict case result is int32 but expected is int64"
+    )
+    def test_constructor_int8_overflow(self):
+        # we silently ignore casting errors as dtype may not apply to all cols
+        vals = [1, 200, 923442]
+
+        result = DataFrame(vals, dtype="int8")
+        expected = DataFrame(vals)
+        tm.assert_frame_equal(result, expected)
+
+        # TODO: these should either both come back as int64 or both as intp,
+        #  not mixed-and-matched on 32bit/windows
+        result = DataFrame({"A": vals}, dtype="int8")
+        expected = DataFrame({"A": vals}, dtype=np.intp)
+        tm.assert_frame_equal(result, expected)
+
     def test_constructor_ordereddict(self):
         import random
 
@@ -896,7 +916,9 @@ def test_constructor_maskedarray(self):
         assert 1.0 == frame["A"][1]
         assert 2.0 == frame["C"][2]
 
-        # what is this even checking??
+    def test_constructor_maskedarray2(self):
+
+        # TODO: what is this even checking??
         mat = ma.masked_all((2, 3), dtype=float)
         frame = DataFrame(mat, columns=["A", "B", "C"], index=[1, 2])
         assert np.all(~np.asarray(frame == frame))
@@ -923,6 +945,7 @@ def test_constructor_maskedarray_nonfloat(self):
         assert 1 == frame["A"][1]
         assert 2 == frame["C"][2]
 
+    def test_constructor_maskedarray_nonfloat2(self):
         # masked np.datetime64 stays (use NaT as null)
         mat = ma.masked_all((2, 3), dtype="M8[ns]")
         # 2-D input
@@ -944,6 +967,8 @@ def test_constructor_maskedarray_nonfloat(self):
         assert 1 == frame["A"].view("i8")[1]
         assert 2 == frame["C"].view("i8")[2]
 
+    def test_constructor_maskedarray_nonfloat3(self):
+
         # masked bool promoted to object
         mat = ma.masked_all((2, 3), dtype=bool)
         # 2-D input
diff --git a/pandas/tests/frame/test_stack_unstack.py b/pandas/tests/frame/test_stack_unstack.py
index 253f416bd6f18..11bb1e3d949e2 100644
--- a/pandas/tests/frame/test_stack_unstack.py
+++ b/pandas/tests/frame/test_stack_unstack.py
@@ -358,7 +358,7 @@ def test_unstack_preserve_dtypes(self):
                 "E": Series([1.0, 50.0, 100.0]).astype("float32"),
                 "F": Series([3.0, 4.0, 5.0]).astype("float64"),
                 "G": False,
-                "H": Series([1, 200, 923442], dtype="int8"),
+                "H": Series([1, -56, 50], dtype="int8"),
             }
         )
 
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index ab484e7ae9d8a..698301374ba38 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -1582,6 +1582,15 @@ def test_construction_from_large_int_scalar_no_overflow(self):
         expected = Series(n)
         tm.assert_series_equal(result, expected)
 
+    def test_constructor_int8_overflow(self):
+        # see also: test_constructor_int8_overflow in frame tests;
+        #  behavior is different here bc dtype is not ignorable
+
+        vals = [1, 200, 923442]
+        msg = "Trying to coerce too-large values to int8"
+        with pytest.raises(OverflowError, match=msg):
+            Series(vals, dtype="int8")
+
     def test_constructor_list_of_periods_infers_period_dtype(self):
         series = Series(list(period_range("2000-01-01", periods=10, freq="D")))
         assert series.dtype == "Period[D]"