diff --git a/xarray/core/computation.py b/xarray/core/computation.py
index f29f6c4dd35..0030cfdcdb9 100644
--- a/xarray/core/computation.py
+++ b/xarray/core/computation.py
@@ -627,22 +627,37 @@ def unified_dim_sizes(
 ) -> dict[Hashable, int]:
     dim_sizes: dict[Hashable, int] = {}
 
+    exclude_dims_lookup = (
+        exclude_dims
+        if isinstance(exclude_dims, (set, frozenset))
+        else set(exclude_dims)
+    )
+
     for var in variables:
-        if len(set(var.dims)) < len(var.dims):
+        dims = var.dims
+        shape = var.shape
+
+        # More efficient duplicate detection: skip set conversion for 0 or 1 dims
+        if len(dims) > 1 and len(set(dims)) < len(dims):
             raise ValueError(
                 "broadcasting cannot handle duplicate "
-                f"dimensions on a variable: {list(var.dims)}"
+                f"dimensions on a variable: {list(dims)}"
             )
-        for dim, size in zip(var.dims, var.shape):
-            if dim not in exclude_dims:
-                if dim not in dim_sizes:
-                    dim_sizes[dim] = size
-                elif dim_sizes[dim] != size:
-                    raise ValueError(
-                        "operands cannot be broadcast together "
-                        "with mismatched lengths for dimension "
-                        f"{dim}: {dim_sizes[dim]} vs {size}"
-                    )
+
+        for i in range(len(dims)):
+            dim = dims[i]
+            if dim in exclude_dims_lookup:
+                continue
+            size = shape[i]
+            existing_size = dim_sizes.get(dim)
+            if existing_size is None:
+                dim_sizes[dim] = size
+            elif existing_size != size:
+                raise ValueError(
+                    "operands cannot be broadcast together "
+                    "with mismatched lengths for dimension "
+                    f"{dim}: {existing_size} vs {size}"
+                )
     return dim_sizes