diff --git a/docs/tutorials/preprocessing.ipynb b/docs/tutorials/preprocessing.ipynb
index e34c399..d3d27b5 100644
--- a/docs/tutorials/preprocessing.ipynb
+++ b/docs/tutorials/preprocessing.ipynb
@@ -179,6 +179,13 @@
     "Next, we compensate the data using the compensation matrix that is included in the FCS file header. Alternatively, one may provide a custom compensation matrix."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The `compensate` function matches the `var_names` of `adata` with the column names of the spillover matrix to compensate the correct channels.  "
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
diff --git a/pytometry/preprocessing/_process_data.py b/pytometry/preprocessing/_process_data.py
index a8a7079..2f630de 100644
--- a/pytometry/preprocessing/_process_data.py
+++ b/pytometry/preprocessing/_process_data.py
@@ -101,21 +101,17 @@ def find_indexes(
 # rename compute bleedthr to compensate
 def compensate(
     adata: AnnData,
-    var_key=None,
-    key="signal_type",
-    comp_matrix=None,
-    matrix_type="spillover",
+    comp_matrix: pd.DataFrame = None,
+    matrix_type: str = "spillover",
     inplace: bool = True,
 ) -> Optional[AnnData]:
     """Computes compensation for data channels.
 
     Args:
         adata (AnnData): AnnData object
-        var_key (str, optional): key where to check if a feature is an area,
-             height etc. type of value. Use `var_names` if None.
         key (str, optional): key where result vector is added
             to the adata.var. Defaults to 'signal_type'.
-        comp_matrix (None, optional): a custom compensation matrix.
+        comp_matrix (pd.DataFrame, optional): a custom compensation matrix.
             Please note that by default we use the spillover matrix directly
             for numeric stability.
         matrix_type (str, optional): whether to use a spillover matrix (default)
@@ -132,8 +128,6 @@ def compensate(
     """
     adata = adata if inplace else adata.copy()
 
-    key_in = key
-
     # locate compensation matrix
     if comp_matrix is not None:
         if matrix_type == "spillover":
@@ -157,22 +151,41 @@ def compensate(
 
     # Ignore channels 'FSC-H', 'FSC-A', 'SSC-H', 'SSC-A',
     # 'FSC-Width', 'Time'
-    if key_in not in adata.var_keys():
-        find_indexes(adata, var_key=var_key, data_type="facs")
-    # select non other indices
-    indexes = np.invert(adata.var[key_in] == "other")
-
-    # To Do:
+    # and compensate only the values indicated in the compensation matrix
+    # Note:
     # the compensation matrix may have different index names than the adata.X matrix
-    # add a check and match for the compensation
-    X_comp = np.linalg.solve(compens, adata.X[:, indexes].T).T
-    adata.X[:, indexes] = X_comp
+    ref_col = adata.var.index
+    idx_in = np.intersect1d(compens.columns, ref_col)
+    if idx_in is None:
+        # try the adata.var['channel'] as reference
+        ref_col = adata.var["channel"]
+        idx_in = np.intersect1d(compens.columns, ref_col)
+        if idx_in is None:
+            raise ValueError(
+                "Could not match the column names of the compensation matrix"
+                'with neither `adata.var.index` nor `adata.var["channel"].'
+            )
+    # match columns of spill mat such that they exactly correspond to adata.var.index
+    ref_names = ref_col[np.in1d(ref_col, idx_in)]
+    query_names = compens.columns[np.in1d(compens.columns, idx_in)]
+    idx_sort = [np.where(query_names == x)[0][0] for x in ref_names]
+    query_idx = np.in1d(compens.columns, query_names)
+    ref_idx = np.in1d(ref_col, ref_names)
+
+    # subset compensation matrix to the columns to run the compensation on
+    compens = compens.iloc[query_idx, query_idx]
+    # sort compensation matrix by adata.var_names
+    compens = compens.iloc[idx_sort, idx_sort]
+    X_comp = np.linalg.solve(compens, adata.X[:, ref_idx].T).T
+    adata.X[:, ref_idx] = X_comp
 
     # check for nan values
-    nan_val = np.isnan(adata.X[:, indexes]).sum()
+    nan_val = np.isnan(adata.X[:, ref_idx]).sum()
     if nan_val > 0:
-        assert f"{nan_val} NaN values found after compensation. Please adjust "
-        "compensation matrix."
+        print(
+            f"{nan_val} NaN values found after compensation. Please adjust "
+            "compensation matrix."
+        )
 
     return None if inplace else adata