diff --git a/src/pyhf/infer/__init__.py b/src/pyhf/infer/__init__.py
index 5aaaf2c1c6..dc5531cd93 100644
--- a/src/pyhf/infer/__init__.py
+++ b/src/pyhf/infer/__init__.py
@@ -61,8 +61,8 @@ def hypotest(
         par_bounds (:obj:`tensor`): The extrema of values the model parameters
             are allowed to reach in the fit.
             The shape should be ``(n, 2)`` for ``n`` model parameters.
-        fixed_params (:obj:`tensor` of :obj:`bool`): The flag to set a parameter constant to its starting
-            value during minimization.
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+            constant to its starting value during minimization.
         calctype (:obj:`str`): The calculator to create. Choose either 'asymptotics' (default) or 'toybased'.
         return_tail_probs (:obj:`bool`): Bool for returning :math:`\mathrm{CL}_{s+b}` and :math:`\mathrm{CL}_{b}`
         return_expected (:obj:`bool`): Bool for returning :math:`\mathrm{CL}_{\mathrm{exp}}`
diff --git a/src/pyhf/infer/calculators.py b/src/pyhf/infer/calculators.py
index ed9642e085..1889dec0c7 100644
--- a/src/pyhf/infer/calculators.py
+++ b/src/pyhf/infer/calculators.py
@@ -61,8 +61,8 @@ def generate_asimov_data(
         par_bounds (:obj:`tensor`): The extrema of values the model parameters
             are allowed to reach in the fit.
             The shape should be ``(n, 2)`` for ``n`` model parameters.
-        fixed_params (:obj:`tensor` of :obj:`bool`): The flag to set a parameter constant to its starting
-            value during minimization.
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+            constant to its starting value during minimization.
         return_fitted_pars (:obj:`bool`): Return the best-fit parameter values for the given ``asimov_mu``.
 
 
@@ -241,8 +241,8 @@ def __init__(
             par_bounds (:obj:`tensor`): The extrema of values the model parameters
                 are allowed to reach in the fit.
                 The shape should be ``(n, 2)`` for ``n`` model parameters.
-            fixed_params (:obj:`tensor` of :obj:`bool`): The flag to set a parameter constant to its starting
-                value during minimization.
+            fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+                constant to its starting value during minimization.
             test_stat (:obj:`str`): The test statistic to use as a numerical summary of the
               data: ``'qtilde'``, ``'q'``, or ``'q0'``.
 
@@ -685,8 +685,8 @@ def __init__(
             par_bounds (:obj:`tensor`): The extrema of values the model parameters
                 are allowed to reach in the fit.
                 The shape should be ``(n, 2)`` for ``n`` model parameters.
-            fixed_params (:obj:`tensor` of :obj:`bool`): The flag to set a parameter constant to its starting
-                value during minimization.
+            fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+                constant to its starting value during minimization.
             test_stat (:obj:`str`): The test statistic to use as a numerical summary of the
               data: ``'qtilde'``, ``'q'``, or ``'q0'``.
 
diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py
index fffff84131..61559b0ed0 100644
--- a/src/pyhf/infer/mle.py
+++ b/src/pyhf/infer/mle.py
@@ -106,8 +106,8 @@ def fit(data, pdf, init_pars=None, par_bounds=None, fixed_params=None, **kwargs)
         par_bounds (:obj:`list` of :obj:`list`/:obj:`tuple`): The extrema of values the model parameters
             are allowed to reach in the fit.
             The shape should be ``(n, 2)`` for ``n`` model parameters.
-        fixed_params (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting
-            value during minimization.
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+            constant to its starting value during minimization.
         kwargs: Keyword arguments passed through to the optimizer API
 
     Returns:
@@ -180,8 +180,8 @@ def fixed_poi_fit(
         par_bounds (:obj:`list` of :obj:`list`/:obj:`tuple`): The extrema of values the model parameters
             are allowed to reach in the fit.
             The shape should be ``(n, 2)`` for ``n`` model parameters.
-        fixed_params (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting
-            value during minimization.
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+            constant to its starting value during minimization.
         kwargs: Keyword arguments passed through to the optimizer API
 
     Returns:
diff --git a/src/pyhf/infer/test_statistics.py b/src/pyhf/infer/test_statistics.py
index cf11e09c86..97b6babe79 100644
--- a/src/pyhf/infer/test_statistics.py
+++ b/src/pyhf/infer/test_statistics.py
@@ -112,8 +112,8 @@ def qmu(mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=F
         par_bounds (:obj:`list` of :obj:`list`/:obj:`tuple`): The extrema of values the model parameters
             are allowed to reach in the fit.
             The shape should be ``(n, 2)`` for ``n`` model parameters.
-        fixed_params (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting
-            value during minimization.
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+            constant to its starting value during minimization.
         return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors
             the fixed-POI and unconstrained fits have converged on
             (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`)
@@ -207,8 +207,8 @@ def qmu_tilde(
         par_bounds (:obj:`list` of :obj:`list`/:obj:`tuple`): The extrema of values the model parameters
             are allowed to reach in the fit.
             The shape should be ``(n, 2)`` for ``n`` model parameters.
-        fixed_params (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting
-            value during minimization.
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+            constant to its starting value during minimization.
         return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors
             the fixed-POI and unconstrained fits have converged on
             (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`)
@@ -290,8 +290,8 @@ def tmu(mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=F
         par_bounds (:obj:`list` of :obj:`list`/:obj:`tuple`): The extrema of values the model parameters
             are allowed to reach in the fit.
             The shape should be ``(n, 2)`` for ``n`` model parameters.
-        fixed_params (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting
-            value during minimization.
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+            constant to its starting value during minimization.
         return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors
             the fixed-POI and unconstrained fits have converged on
             (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`)
@@ -380,8 +380,8 @@ def tmu_tilde(
         par_bounds (:obj:`list` of :obj:`list`/:obj:`tuple`): The extrema of values the model parameters
             are allowed to reach in the fit.
             The shape should be ``(n, 2)`` for ``n`` model parameters.
-        fixed_params (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting
-            value during minimization.
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+            constant to its starting value during minimization.
         return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors
             the fixed-POI and unconstrained fits have converged on
             (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`)
@@ -458,8 +458,8 @@ def q0(mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=Fa
         par_bounds (:obj:`list` of :obj:`list`/:obj:`tuple`): The extrema of values the model parameters
             are allowed to reach in the fit.
             The shape should be ``(n, 2)`` for ``n`` model parameters.
-        fixed_params (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting
-            value during minimization.
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): The flag to set a parameter
+            constant to its starting value during minimization.
         return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors
             the fixed-POI and unconstrained fits have converged on
             (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`)
diff --git a/src/pyhf/infer/utils.py b/src/pyhf/infer/utils.py
index 1131b01de9..a9eeefac49 100644
--- a/src/pyhf/infer/utils.py
+++ b/src/pyhf/infer/utils.py
@@ -22,7 +22,7 @@ def all_pois_floating(pdf, fixed_params):
     Args:
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema
          ``model.json``.
-        fixed_params (:obj:`list` or `tensor` of :obj:`bool`): Array of
+        fixed_params (:obj:`tuple` or :obj:`list` of :obj:`bool`): Array of
          :obj:`bool` indicating if model parameters are fixed.
 
     Returns: