diff --git a/src/compressed_tensors/quantization/quant_scheme.py b/src/compressed_tensors/quantization/quant_scheme.py
index 36b886044..9fcc0d55d 100644
--- a/src/compressed_tensors/quantization/quant_scheme.py
+++ b/src/compressed_tensors/quantization/quant_scheme.py
@@ -142,6 +142,18 @@ def is_preset_scheme(name: str) -> bool:
     ),
 )
 
+# 4 bit integer weights only asymmetric quantization
+W4A16_ASYM = dict(
+    weights=QuantizationArgs(
+        num_bits=4,
+        type=QuantizationType.INT,
+        strategy=QuantizationStrategy.GROUP,
+        group_size=128,
+        symmetric=False,
+        dynamic=False,
+    ),
+)
+
 # 4 bit integer weights and 8 bit activations quantization
 INT8_W4A8 = dict(
     weights=QuantizationArgs(
@@ -205,6 +217,7 @@ def is_preset_scheme(name: str) -> bool:
     # Integer weight only schemes
     "W8A16": W8A16,
     "W4A16": W4A16,
+    "W4A16_ASYM": W4A16_ASYM,
     # Integer weight and activation schemes
     "W8A8": INT8_W8A8,
     "INT8": INT8_W8A8,  # alias for W8A8
diff --git a/src/compressed_tensors/quantization/utils/helpers.py b/src/compressed_tensors/quantization/utils/helpers.py
index 9f65ee330..d7e6d5f81 100644
--- a/src/compressed_tensors/quantization/utils/helpers.py
+++ b/src/compressed_tensors/quantization/utils/helpers.py
@@ -64,8 +64,11 @@ def calculate_qparams(
     :param quantization_args: settings to quantization
     :return: tuple of the calculated scale(s) and zero point(s)
     """
+    # based on the implementations for consuming quantized values,
+    # 0.0 must always be representable within the quantized range
     min_vals = torch.min(min_vals, torch.zeros_like(min_vals))
     max_vals = torch.max(max_vals, torch.zeros_like(max_vals))
+
     device = min_vals.device
 
     bit_min, bit_max = calculate_range(quantization_args, device)
@@ -84,6 +87,9 @@ def calculate_qparams(
         zero_points = torch.clamp(zero_points, bit_min, bit_max)
 
     # match zero-points to quantized type
+    # if casting to int, use round instead of truncate
+    if quantization_args.type == QuantizationType.INT:
+        zero_points = torch.round(zero_points)
     zero_points = zero_points.to(zp_dtype)
 
     if scales.ndim == 0:
@@ -96,7 +102,7 @@ def calculate_qparams(
 def compute_dynamic_scales_and_zp(value: Tensor, args: QuantizationArgs):
     """
     Returns the computed scales and zero points for dynamic activation
-    qunatization.
+    quantization.
 
     :param value: tensor to calculate quantization parameters for
     :param args: quantization args