diff --git a/src/params.cpp b/src/params.cpp
index c14bb4b4..20548c2d 100644
--- a/src/params.cpp
+++ b/src/params.cpp
@@ -858,21 +858,23 @@ static bool GetTimeInfo(Cursor* cur, Py_ssize_t index, PyObject* param, ParamInf
 }
 
 
-inline bool NeedsBigInt(PyObject* p)
+inline bool NeedsBigInt(long long ll)
 {
     // NOTE: Smallest 32-bit int should be -214748368 but the MS compiler v.1900 AMD64
     // says that (10 < -2147483648).  Perhaps I miscalculated the minimum?
-    long long ll = PyLong_AsLongLong(p);
     return ll < -2147483647 || ll > 2147483647;
 }
 
 #if PY_MAJOR_VERSION < 3
 static bool GetIntInfo(Cursor* cur, Py_ssize_t index, PyObject* param, ParamInfo& info, bool isTVP)
 {
-    if (isTVP || NeedsBigInt(param))
-    {
-        info.Data.i64 = (INT64)PyLong_AsLongLong(param);
+    long long value = PyLong_AsLongLong(param);
+    if (PyErr_Occurred())
+        return false;
 
+    if (isTVP || NeedsBigInt(value))
+    {
+        info.Data.i64          = (INT64)value;
         info.ValueType         = SQL_C_SBIGINT;
         info.ParameterType     = SQL_BIGINT;
         info.ParameterValuePtr = &info.Data.i64;
@@ -880,14 +882,12 @@ static bool GetIntInfo(Cursor* cur, Py_ssize_t index, PyObject* param, ParamInfo
     }
     else
     {
-        info.Data.i32 = (int)PyLong_AsLong(param);
-
+        info.Data.i32          = (int)value;
         info.ValueType         = SQL_C_LONG;
         info.ParameterType     = SQL_INTEGER;
         info.ParameterValuePtr = &info.Data.i32;
         info.StrLen_or_Ind     = 4;
     }
-
     return true;
 }
 #endif
@@ -898,10 +898,13 @@ static bool GetLongInfo(Cursor* cur, Py_ssize_t index, PyObject* param, ParamInf
     // Unfortunately this may mean that we end up with two execution plans for the same SQL.
     // We could use SQLDescribeParam but that's kind of expensive.
 
-    if (isTVP || NeedsBigInt(param))
-    {
-        info.Data.i64 = (INT64)PyLong_AsLongLong(param);
+    long long value = PyLong_AsLongLong(param);
+    if (PyErr_Occurred())
+        return false;
 
+    if (isTVP || NeedsBigInt(value))
+    {
+        info.Data.i64          = (INT64)value;
         info.ValueType         = SQL_C_SBIGINT;
         info.ParameterType     = SQL_BIGINT;
         info.ParameterValuePtr = &info.Data.i64;
@@ -909,22 +912,26 @@ static bool GetLongInfo(Cursor* cur, Py_ssize_t index, PyObject* param, ParamInf
     }
     else
     {
-        info.Data.i32 = (int)PyLong_AsLong(param);
-
+        info.Data.i32          = (int)value;
         info.ValueType         = SQL_C_LONG;
         info.ParameterType     = SQL_INTEGER;
         info.ParameterValuePtr = &info.Data.i32;
         info.StrLen_or_Ind     = 4;
     }
-
     return true;
 }
 
 static bool GetFloatInfo(Cursor* cur, Py_ssize_t index, PyObject* param, ParamInfo& info)
 {
-    // TODO: Overflow?
-    info.Data.dbl = PyFloat_AsDouble(param);
+    // Python floats are usually numeric values, but can also be "Infinity" or "NaN".
+    // https://docs.python.org/3/library/functions.html#float
+    // PyFloat_AsDouble() does not generate an error for Infinity/NaN, and it is not
+    // easy to check for those values.  Typically, the database will reject them.
+    double value = PyFloat_AsDouble(param);
+    if (PyErr_Occurred())
+        return false;
 
+    info.Data.dbl          = value;
     info.ValueType         = SQL_C_DOUBLE;
     info.ParameterType     = SQL_DOUBLE;
     info.ParameterValuePtr = &info.Data.dbl;
diff --git a/tests2/sqlservertests.py b/tests2/sqlservertests.py
index e00d15fc..3ffbbcfb 100755
--- a/tests2/sqlservertests.py
+++ b/tests2/sqlservertests.py
@@ -891,6 +891,15 @@ def test_bigint(self):
         result = self.cursor.execute("select d from t1").fetchone()[0]
         self.assertEqual(result, input)
 
+    def test_overflow_int(self):
+        # python allows integers of any size, bigger than an 8 byte int can contain
+        input = 9999999999999999999999999999999999999
+        self.cursor.execute("create table t1(d bigint)")
+        self.cnxn.commit()
+        self.assertRaises(OverflowError, self.cursor.execute, "insert into t1 values (?)", input)
+        result = self.cursor.execute("select * from t1").fetchall()
+        self.assertEqual(result, [])
+
     def test_float(self):
         value = 1234.567
         self.cursor.execute("create table t1(n float)")
@@ -912,6 +921,14 @@ def test_negative_float(self):
         result  = self.cursor.execute("select n from t1").fetchone()[0]
         self.assertEqual(value, result)
 
+    def test_non_numeric_float(self):
+        self.cursor.execute("create table t1(d float)")
+        self.cnxn.commit()
+        for input in (float('+Infinity'), float('-Infinity'), float('NaN')):
+            self.assertRaises(pyodbc.ProgrammingError, self.cursor.execute, "insert into t1 values (?)", input)
+        result = self.cursor.execute("select * from t1").fetchall()
+        self.assertEqual(result, [])
+
 
     #
     # stored procedures
diff --git a/tests3/sqlservertests.py b/tests3/sqlservertests.py
index 5a52b732..cc1854f3 100644
--- a/tests3/sqlservertests.py
+++ b/tests3/sqlservertests.py
@@ -783,6 +783,15 @@ def test_bigint(self):
         result = self.cursor.execute("select d from t1").fetchone()[0]
         self.assertEqual(result, input)
 
+    def test_overflow_int(self):
+        # python allows integers of any size, bigger than an 8 byte int can contain
+        input = 9999999999999999999999999999999999999
+        self.cursor.execute("create table t1(d bigint)")
+        self.cnxn.commit()
+        self.assertRaises(OverflowError, self.cursor.execute, "insert into t1 values (?)", input)
+        result = self.cursor.execute("select * from t1").fetchall()
+        self.assertEqual(result, [])
+
     def test_float(self):
         value = 1234.567
         self.cursor.execute("create table t1(n float)")
@@ -804,6 +813,14 @@ def test_negative_float(self):
         result  = self.cursor.execute("select n from t1").fetchone()[0]
         self.assertEqual(value, result)
 
+    def test_non_numeric_float(self):
+        self.cursor.execute("create table t1(d float)")
+        self.cnxn.commit()
+        for input in (float('+Infinity'), float('-Infinity'), float('NaN')):
+            self.assertRaises(pyodbc.ProgrammingError, self.cursor.execute, "insert into t1 values (?)", input)
+        result = self.cursor.execute("select * from t1").fetchall()
+        self.assertEqual(result, [])
+
     #
     # stored procedures
     #