diff --git a/docs/workflows.rst b/docs/workflows.rst
index 3988a40dc..dbec7f7fe 100644
--- a/docs/workflows.rst
+++ b/docs/workflows.rst
@@ -568,8 +568,8 @@ A visualization of the AROMA component classification is also included in the HT
 
 .. _bold_t2s:
 
-T2* Driven Coregistration
-~~~~~~~~~~~~~~~~~~~~~~~~~
+T2*-driven echo combination
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
 :py:func:`~fmriprep.workflows.bold.t2s.init_bold_t2s_wf`
 
 If multi-echo :abbr:`BOLD (blood-oxygen level-dependent)` data is supplied,
diff --git a/fmriprep/interfaces/multiecho.py b/fmriprep/interfaces/multiecho.py
index 8ef963bff..25fb12ec7 100644
--- a/fmriprep/interfaces/multiecho.py
+++ b/fmriprep/interfaces/multiecho.py
@@ -16,7 +16,6 @@
 
 """
 import os
-from nibabel.filename_parser import splitext_addext
 
 from nipype import logging
 from nipype.interfaces.base import (
@@ -39,13 +38,21 @@ class T2SMapInputSpec(CommandLineInputSpec):
                              mandatory=True,
                              minlen=3,
                              desc='echo times')
+    fittype = traits.Enum('curvefit', 'loglin',
+                          argstr='--fittype %s',
+                          position=3,
+                          usedefault=True,
+                          desc=('Desired fitting method: '
+                                '"loglin" means that a linear model is fit '
+                                'to the log of the data. '
+                                '"curvefit" means that a more computationally '
+                                'demanding monoexponential model is fit '
+                                'to the raw data.'))
 
 
 class T2SMapOutputSpec(TraitedSpec):
     t2star_map = File(exists=True, desc='limited T2* map')
-    s0_map = File(exists=True, desc='limited s0 map')
-    t2star_adaptive_map = File(exists=True, desc='adaptive T2* map')
-    s0_adaptive_map = File(exists=True, desc='adaptive s0 map')
+    s0_map = File(exists=True, desc='limited S0 map')
     optimal_comb = File(exists=True, desc='optimally combined ME-EPI time series')
 
 
@@ -64,7 +71,7 @@ class T2SMap(CommandLine):
     >>> t2smap.inputs.echo_times = [0.013, 0.027, 0.043]
     >>> t2smap.cmdline  # doctest: +ELLIPSIS
     't2smap -d sub-01_run-01_echo-1_bold.nii.gz sub-01_run-01_echo-2_bold.nii.gz \
-sub-01_run-01_echo-3_bold.nii.gz -e 13.0 27.0 43.0'
+sub-01_run-01_echo-3_bold.nii.gz -e 13.0 27.0 43.0 --fittype curvefit'
     """
     _cmd = 't2smap'
     input_spec = T2SMapInputSpec
@@ -77,13 +84,8 @@ def _format_arg(self, name, trait_spec, value):
 
     def _list_outputs(self):
         outputs = self._outputs().get()
-        filename = splitext_addext(os.path.basename(self.inputs.in_files[0]))[0]
-        out_dir = os.path.abspath('TED.{}'.format(filename))
-
-        outputs['t2star_map'] = os.path.join(out_dir, 't2sv.nii')
-        outputs['s0_map'] = os.path.join(out_dir, 's0v.nii')
-        outputs['t2star_adaptive_map'] = os.path.join(out_dir, 't2svG.nii')
-        outputs['s0_adaptive_map'] = os.path.join(out_dir, 's0vG.nii')
-        outputs['optimal_comb'] = os.path.join(out_dir, 'ts_OC.nii')
-
+        out_dir = os.getcwd()
+        outputs['t2star_map'] = os.path.join(out_dir, 'T2starmap.nii.gz')
+        outputs['s0_map'] = os.path.join(out_dir, 'S0map.nii.gz')
+        outputs['optimal_comb'] = os.path.join(out_dir, 'desc-optcom_bold.nii.gz')
         return outputs
diff --git a/fmriprep/workflows/bold/t2s.py b/fmriprep/workflows/bold/t2s.py
index 643a6acd6..fd62a830c 100644
--- a/fmriprep/workflows/bold/t2s.py
+++ b/fmriprep/workflows/bold/t2s.py
@@ -61,7 +61,8 @@ def init_bold_t2s_wf(echo_times, mem_gb, omp_nthreads,
     workflow = Workflow(name=name)
     workflow.__desc__ = """\
 A T2* map was estimated from the preprocessed BOLD by fitting to a monoexponential signal
-decay model with log-linear regression.
+decay model with nonlinear regression, using T2*/S0 estimates from a log-linear
+regression fit as initial values.
 For each voxel, the maximal number of echoes with reliable signal in that voxel were
 used to fit the model.
 The calculated T2* map was then used to optimally combine preprocessed BOLD across
diff --git a/setup.cfg b/setup.cfg
index de49db581..1a7777b5c 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -35,7 +35,7 @@ install_requires =
     pyyaml
     sdcflows @ git+https://github.com/nipreps/sdcflows.git@master
     smriprep @ git+https://github.com/poldracklab/smriprep.git@master
-    tedana >= 0.0.5
+    tedana >= 0.0.9a1, < 0.0.10
     templateflow ~= 0.6
     toml
 test_requires =