diff --git a/ixmp4/data/db/optimization/parameter/model.py b/ixmp4/data/db/optimization/parameter/model.py
index 3199675d..bb052ea7 100644
--- a/ixmp4/data/db/optimization/parameter/model.py
+++ b/ixmp4/data/db/optimization/parameter/model.py
@@ -4,6 +4,7 @@
 from sqlalchemy.orm import validates
 
 from ixmp4 import db
+from ixmp4.core.exceptions import OptimizationDataValidationError
 from ixmp4.data import types
 from ixmp4.data.abstract import optimization as abstract
 
@@ -14,6 +15,7 @@ class Parameter(base.BaseModel):
     # NOTE: These might be mixin-able, but would require some abstraction
     NotFound: ClassVar = abstract.Parameter.NotFound
     NotUnique: ClassVar = abstract.Parameter.NotUnique
+    DataInvalid: ClassVar = OptimizationDataValidationError
     DeletionPrevented: ClassVar = abstract.Parameter.DeletionPrevented
 
     # constrained_to_indexsets: ClassVar[list[str] | None] = None
@@ -28,7 +30,7 @@ def validate_data(self, key, data: dict[str, Any]):
         del data_to_validate["values"]
         del data_to_validate["units"]
         _ = utils.validate_data(
-            key=key,
+            host=self,
             data=data_to_validate,
             columns=self.columns,
         )
diff --git a/ixmp4/data/db/optimization/parameter/repository.py b/ixmp4/data/db/optimization/parameter/repository.py
index f4cbb85f..699cfcf4 100644
--- a/ixmp4/data/db/optimization/parameter/repository.py
+++ b/ixmp4/data/db/optimization/parameter/repository.py
@@ -3,6 +3,7 @@
 import pandas as pd
 
 from ixmp4 import db
+from ixmp4.core.exceptions import OptimizationItemUsageError
 from ixmp4.data.abstract import optimization as abstract
 from ixmp4.data.auth.decorators import guard
 from ixmp4.data.db.unit import Unit
@@ -20,6 +21,8 @@ class ParameterRepository(
 ):
     model_class = Parameter
 
+    UsageError = OptimizationItemUsageError
+
     def __init__(self, *args, **kwargs) -> None:
         super().__init__(*args, **kwargs)
         self.docs = ParameterDocsRepository(*args, **kwargs)
@@ -112,16 +115,20 @@ def create(
         if isinstance(constrained_to_indexsets, str):
             constrained_to_indexsets = list(constrained_to_indexsets)
         if column_names and len(column_names) != len(constrained_to_indexsets):
-            raise ValueError(
+            raise self.UsageError(
+                f"While processing Parameter {name}: \n"
                 "`constrained_to_indexsets` and `column_names` not equal in length! "
                 "Please provide the same number of entries for both!"
             )
         # TODO: activate something like this if each column must be indexed by a unique
         # indexset
         # if len(constrained_to_indexsets) != len(set(constrained_to_indexsets)):
-        #     raise ValueError("Each dimension must be constrained to a unique indexset!") # noqa
+        #     raise self.UsageError("Each dimension must be constrained to a unique indexset!") # noqa
         if column_names and len(column_names) != len(set(column_names)):
-            raise ValueError("The given `column_names` are not unique!")
+            raise self.UsageError(
+                f"While processing Parameter {name}: \n"
+                "The given `column_names` are not unique!"
+            )
 
         parameter = super().create(
             run_id=run_id,
@@ -149,13 +156,19 @@ def tabulate(self, *args, **kwargs) -> pd.DataFrame:
     @guard("edit")
     def add_data(self, parameter_id: int, data: dict[str, Any] | pd.DataFrame) -> None:
         if isinstance(data, dict):
-            data = pd.DataFrame.from_dict(data=data)
+            try:
+                data = pd.DataFrame.from_dict(data=data)
+            except ValueError as e:
+                raise Parameter.DataInvalid(str(e)) from e
+
         parameter = self.get_by_id(id=parameter_id)
 
         missing_columns = set(["values", "units"]) - set(data.columns)
-        assert (
-            not missing_columns
-        ), f"Parameter.data must include the column(s): {', '.join(missing_columns)}!"
+        if missing_columns:
+            raise OptimizationItemUsageError(
+                "Parameter.data must include the column(s): "
+                f"{', '.join(missing_columns)}!"
+            )
 
         # Can use a set for now, need full column if we care about order
         for unit_name in set(data["units"]):
diff --git a/tests/core/test_optimization_parameter.py b/tests/core/test_optimization_parameter.py
index e0f92768..8602ddf1 100644
--- a/tests/core/test_optimization_parameter.py
+++ b/tests/core/test_optimization_parameter.py
@@ -3,6 +3,10 @@
 
 import ixmp4
 from ixmp4.core import IndexSet, Parameter
+from ixmp4.core.exceptions import (
+    OptimizationDataValidationError,
+    OptimizationItemUsageError,
+)
 
 from ..utils import assert_unordered_equality, create_indexsets_for_run
 
@@ -60,7 +64,7 @@ def test_create_parameter(self, platform: ixmp4.Platform):
             )
 
         # Test mismatch in constrained_to_indexsets and column_names raises
-        with pytest.raises(ValueError, match="not equal in length"):
+        with pytest.raises(OptimizationItemUsageError, match="not equal in length"):
             _ = run.optimization.parameters.create(
                 "Parameter 2",
                 constrained_to_indexsets=[indexset.name],
@@ -76,7 +80,9 @@ def test_create_parameter(self, platform: ixmp4.Platform):
         assert parameter_2.columns[0].name == "Column 1"
 
         # Test duplicate column_names raise
-        with pytest.raises(ValueError, match="`column_names` are not unique"):
+        with pytest.raises(
+            OptimizationItemUsageError, match="`column_names` are not unique"
+        ):
             _ = run.optimization.parameters.create(
                 name="Parameter 3",
                 constrained_to_indexsets=[indexset.name, indexset.name],
@@ -149,7 +155,7 @@ def test_parameter_add_data(self, platform: ixmp4.Platform):
         )
 
         with pytest.raises(
-            AssertionError, match=r"must include the column\(s\): values!"
+            OptimizationItemUsageError, match=r"must include the column\(s\): values!"
         ):
             parameter_2.add(
                 pd.DataFrame(
@@ -162,7 +168,7 @@ def test_parameter_add_data(self, platform: ixmp4.Platform):
             )
 
         with pytest.raises(
-            AssertionError, match=r"must include the column\(s\): units!"
+            OptimizationItemUsageError, match=r"must include the column\(s\): units!"
         ):
             parameter_2.add(
                 data=pd.DataFrame(
@@ -176,7 +182,10 @@ def test_parameter_add_data(self, platform: ixmp4.Platform):
 
         # By converting data to pd.DataFrame, we automatically enforce equal length
         # of new columns, raises All arrays must be of the same length otherwise:
-        with pytest.raises(ValueError, match="All arrays must be of the same length"):
+        with pytest.raises(
+            OptimizationDataValidationError,
+            match="All arrays must be of the same length",
+        ):
             parameter_2.add(
                 data={
                     indexset.name: ["foo", "foo"],
@@ -186,7 +195,9 @@ def test_parameter_add_data(self, platform: ixmp4.Platform):
                 },
             )
 
-        with pytest.raises(ValueError, match="contains duplicate rows"):
+        with pytest.raises(
+            OptimizationDataValidationError, match="contains duplicate rows"
+        ):
             parameter_2.add(
                 data={
                     indexset.name: ["foo", "foo"],
diff --git a/tests/data/test_optimization_parameter.py b/tests/data/test_optimization_parameter.py
index 7365da34..dac17e86 100644
--- a/tests/data/test_optimization_parameter.py
+++ b/tests/data/test_optimization_parameter.py
@@ -2,6 +2,10 @@
 import pytest
 
 import ixmp4
+from ixmp4.core.exceptions import (
+    OptimizationDataValidationError,
+    OptimizationItemUsageError,
+)
 from ixmp4.data.abstract import Parameter
 
 from ..utils import assert_unordered_equality, create_indexsets_for_run
@@ -60,7 +64,7 @@ def test_create_parameter(self, platform: ixmp4.Platform):
             )
 
         # Test mismatch in constrained_to_indexsets and column_names raises
-        with pytest.raises(ValueError, match="not equal in length"):
+        with pytest.raises(OptimizationItemUsageError, match="not equal in length"):
             _ = platform.backend.optimization.parameters.create(
                 run_id=run.id,
                 name="Parameter 2",
@@ -78,7 +82,9 @@ def test_create_parameter(self, platform: ixmp4.Platform):
         assert parameter_2.columns[0].name == "Column 1"
 
         # Test duplicate column_names raise
-        with pytest.raises(ValueError, match="`column_names` are not unique"):
+        with pytest.raises(
+            OptimizationItemUsageError, match="`column_names` are not unique"
+        ):
             _ = platform.backend.optimization.parameters.create(
                 run_id=run.id,
                 name="Parameter 3",
@@ -161,7 +167,7 @@ def test_parameter_add_data(self, platform: ixmp4.Platform):
         )
 
         with pytest.raises(
-            AssertionError, match=r"must include the column\(s\): values!"
+            OptimizationItemUsageError, match=r"must include the column\(s\): values!"
         ):
             platform.backend.optimization.parameters.add_data(
                 parameter_id=parameter_2.id,
@@ -175,7 +181,7 @@ def test_parameter_add_data(self, platform: ixmp4.Platform):
             )
 
         with pytest.raises(
-            AssertionError, match=r"must include the column\(s\): units!"
+            OptimizationItemUsageError, match=r"must include the column\(s\): units!"
         ):
             platform.backend.optimization.parameters.add_data(
                 parameter_id=parameter_2.id,
@@ -190,7 +196,10 @@ def test_parameter_add_data(self, platform: ixmp4.Platform):
 
         # By converting data to pd.DataFrame, we automatically enforce equal length
         # of new columns, raises All arrays must be of the same length otherwise:
-        with pytest.raises(ValueError, match="All arrays must be of the same length"):
+        with pytest.raises(
+            OptimizationDataValidationError,
+            match="All arrays must be of the same length",
+        ):
             platform.backend.optimization.parameters.add_data(
                 parameter_id=parameter_2.id,
                 data={
@@ -201,7 +210,9 @@ def test_parameter_add_data(self, platform: ixmp4.Platform):
                 },
             )
 
-        with pytest.raises(ValueError, match="contains duplicate rows"):
+        with pytest.raises(
+            OptimizationDataValidationError, match="contains duplicate rows"
+        ):
             platform.backend.optimization.parameters.add_data(
                 parameter_id=parameter_2.id,
                 data={