diff --git a/mapper.go b/mapper.go
index a605dea..d038cb0 100644
--- a/mapper.go
+++ b/mapper.go
@@ -3,6 +3,7 @@ package kong
 import (
 	"encoding"
 	"encoding/json"
+	"fmt"
 	"io/ioutil"
 	"math/bits"
 	"net/url"
@@ -325,23 +326,22 @@ func intDecoder(bits int) MapperFunc { // nolint: dupl
 		if err != nil {
 			return err
 		}
+		var sv string
 		switch v := t.Value.(type) {
 		case string:
-			n, err := strconv.ParseInt(v, 10, bits)
-			if err != nil {
-				return errors.Errorf("expected an int but got %q (%T)", t, t.Value)
-			}
-			target.SetInt(n)
+			sv = v
 
-		case float64:
-			target.SetInt(int64(v))
-
-		case int, int8, int16, int32, int64, uint, uint8, uint16, uint32, uint64:
-			target.Set(reflect.ValueOf(v))
+		case int, int8, int16, int32, int64, uint, uint8, uint16, uint32, uint64, float32, float64:
+			sv = fmt.Sprintf("%v", v)
 
 		default:
 			return errors.Errorf("expected an int but got %q (%T)", t, t.Value)
 		}
+		n, err := strconv.ParseInt(sv, 10, bits)
+		if err != nil {
+			return errors.Errorf("expected a valid %d bit int but got %q", bits, sv)
+		}
+		target.SetInt(n)
 		return nil
 	}
 }
@@ -352,23 +352,22 @@ func uintDecoder(bits int) MapperFunc { // nolint: dupl
 		if err != nil {
 			return err
 		}
+		var sv string
 		switch v := t.Value.(type) {
 		case string:
-			n, err := strconv.ParseUint(v, 10, bits)
-			if err != nil {
-				return errors.Errorf("expected a uint but got %q (%T)", t, t.Value)
-			}
-			target.SetUint(n)
+			sv = v
 
-		case float64:
-			target.SetUint(uint64(v))
-
-		case int, int8, int16, int32, int64, uint, uint8, uint16, uint32, uint64:
-			target.Set(reflect.ValueOf(v))
+		case int, int8, int16, int32, int64, uint, uint8, uint16, uint32, uint64, float32, float64:
+			sv = fmt.Sprintf("%v", v)
 
 		default:
 			return errors.Errorf("expected an int but got %q (%T)", t, t.Value)
 		}
+		n, err := strconv.ParseUint(sv, 10, bits)
+		if err != nil {
+			return errors.Errorf("expected a valid %d bit uint but got %q", bits, sv)
+		}
+		target.SetUint(n)
 		return nil
 	}
 }
diff --git a/mapper_test.go b/mapper_test.go
index 25e09c4..9996b24 100644
--- a/mapper_test.go
+++ b/mapper_test.go
@@ -5,6 +5,7 @@ import (
 	"encoding/json"
 	"fmt"
 	"io/ioutil"
+	"math"
 	"net/url"
 	"os"
 	"reflect"
@@ -260,3 +261,66 @@ func TestCounter(t *testing.T) {
 	require.NoError(t, err)
 	require.Equal(t, 3., cli.Float)
 }
+
+func TestNumbers(t *testing.T) {
+	type CLI struct {
+		F32 float32
+		F64 float64
+		I8  int8
+		I16 int16
+		I32 int32
+		I64 int64
+		U8  uint8
+		U16 uint16
+		U32 uint32
+		U64 uint64
+	}
+	var cli CLI
+	p := mustNew(t, &cli)
+	t.Run("Max", func(t *testing.T) {
+		_, err := p.Parse([]string{
+			"--f-32", fmt.Sprintf("%v", math.MaxFloat32),
+			"--f-64", fmt.Sprintf("%v", math.MaxFloat64),
+			"--i-8", fmt.Sprintf("%v", math.MaxInt8),
+			"--i-16", fmt.Sprintf("%v", math.MaxInt16),
+			"--i-32", fmt.Sprintf("%v", math.MaxInt32),
+			"--i-64", fmt.Sprintf("%v", math.MaxInt64),
+			"--u-8", fmt.Sprintf("%v", math.MaxUint8),
+			"--u-16", fmt.Sprintf("%v", math.MaxUint16),
+			"--u-32", fmt.Sprintf("%v", math.MaxUint32),
+			"--u-64", fmt.Sprintf("%v", uint64(math.MaxUint64)),
+		})
+		require.NoError(t, err)
+		require.Equal(t, CLI{
+			F32: math.MaxFloat32,
+			F64: math.MaxFloat64,
+			I8:  math.MaxInt8,
+			I16: math.MaxInt16,
+			I32: math.MaxInt32,
+			I64: math.MaxInt64,
+			U8:  math.MaxUint8,
+			U16: math.MaxUint16,
+			U32: math.MaxUint32,
+			U64: math.MaxUint64,
+		}, cli)
+	})
+	t.Run("Min", func(t *testing.T) {
+		_, err := p.Parse([]string{
+			fmt.Sprintf("--i-8=%v", math.MinInt8),
+			fmt.Sprintf("--i-16=%v", math.MinInt16),
+			fmt.Sprintf("--i-32=%v", math.MinInt32),
+			fmt.Sprintf("--i-64=%v", math.MinInt64),
+			fmt.Sprintf("--u-8=%v", 0),
+			fmt.Sprintf("--u-16=%v", 0),
+			fmt.Sprintf("--u-32=%v", 0),
+			fmt.Sprintf("--u-64=%v", 0),
+		})
+		require.NoError(t, err)
+		require.Equal(t, CLI{
+			I8:  math.MinInt8,
+			I16: math.MinInt16,
+			I32: math.MinInt32,
+			I64: math.MinInt64,
+		}, cli)
+	})
+}